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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | none | [
"none"
] | null | null | Appleman has a very big sheet of paper. This sheet has a form of rectangle with dimensions 1<=×<=*n*. Your task is help Appleman with folding of such a sheet. Actually, you need to perform *q* queries. Each query will have one of the following types:
1. Fold the sheet of paper at position *p**i*. After this query the leftmost part of the paper with dimensions 1<=×<=*p**i* must be above the rightmost part of the paper with dimensions 1<=×<=([*current* *width* *of* *sheet*]<=-<=*p**i*). 1. Count what is the total width of the paper pieces, if we will make two described later cuts and consider only the pieces between the cuts. We will make one cut at distance *l**i* from the left border of the current sheet of paper and the other at distance *r**i* from the left border of the current sheet of paper.
Please look at the explanation of the first test example for better understanding of the problem. | The first line contains two integers: *n* and *q* (1<=<=≤<=*n*<=≤<=105; 1<=≤<=*q*<=≤<=105) — the width of the paper and the number of queries.
Each of the following *q* lines contains one of the described queries in the following format:
- "1 *p**i*" (1<=≤<=*p**i*<=<<=[*current* *width* *of* *sheet*]) — the first type query. - "2 *l**i* *r**i*" (0<=≤<=*l**i*<=<<=*r**i*<=≤<=[*current* *width* *of* *sheet*]) — the second type query. | For each query of the second type, output the answer. | [
"7 4\n1 3\n1 2\n2 0 1\n2 1 2\n",
"10 9\n2 2 9\n1 1\n2 0 1\n1 8\n2 0 8\n1 2\n2 1 3\n1 4\n2 2 4\n"
] | [
"4\n3\n",
"7\n2\n10\n4\n5\n"
] | The pictures below show the shapes of the paper during the queries of the first example:
After the first fold operation the sheet has width equal to 4, after the second one the width of the sheet equals to 2. | [] | 62 | 0 | 0 | 12,849 |
|
863 | Turn Off The TV | [
"data structures",
"sortings"
] | null | null | Luba needs your help again! Luba has *n* TV sets. She knows that *i*-th TV set will be working from moment of time *l**i* till moment *r**i*, inclusive.
Luba wants to switch off one of TV sets in order to free the socket. Let's call some TV set redundant if after switching it off the number of integer moments of time when at least one of TV sets is working won't decrease. Luba will be very upset if she has to switch off a non-redundant TV set.
Help Luba by telling her the index of some redundant TV set. If there is no any, print -1. | The first line contains one integer number *n* (1<=≤<=*n*<=≤<=2·105) — the number of TV sets.
Then *n* lines follow, each of them containing two integer numbers *l**i*,<=*r**i* (0<=≤<=*l**i*<=≤<=*r**i*<=≤<=109) denoting the working time of *i*-th TV set. | If there is no any redundant TV set, print -1. Otherwise print the index of any redundant TV set (TV sets are indexed from 1 to *n*).
If there are multiple answers, print any of them. | [
"3\n1 3\n4 6\n1 7\n",
"2\n0 10\n0 10\n",
"3\n1 2\n3 4\n6 8\n",
"3\n1 2\n2 3\n3 4\n"
] | [
"1\n",
"1\n",
"-1\n",
"2\n"
] | Consider the first sample. Initially all integer moments of time such that at least one TV set is working are from the segment [1;7]. It's easy to see that this segment won't change if we switch off the first TV set (or the second one).
Note that in the fourth sample you can switch off the second TV set, since even without it all integer moments such that any of the TV sets is working denote the segment [1;4]. | [
{
"input": "3\n1 3\n4 6\n1 7",
"output": "1"
},
{
"input": "2\n0 10\n0 10",
"output": "1"
},
{
"input": "3\n1 2\n3 4\n6 8",
"output": "-1"
},
{
"input": "3\n1 2\n2 3\n3 4",
"output": "2"
},
{
"input": "3\n0 500000000\n500000001 1000000000\n0 1000000000",
"output": "1"
},
{
"input": "3\n1 5\n2 4\n6 10",
"output": "2"
},
{
"input": "10\n4 4\n5 9\n5 7\n2 8\n6 10\n4 10\n1 3\n8 9\n0 0\n5 7",
"output": "1"
},
{
"input": "2\n1 3\n2 4",
"output": "-1"
},
{
"input": "1\n8 9",
"output": "-1"
},
{
"input": "8\n13 17\n83 89\n31 33\n7 13\n52 52\n88 89\n29 30\n16 22",
"output": "6"
},
{
"input": "4\n63 63\n12 34\n17 29\n58 91",
"output": "1"
},
{
"input": "3\n1 10\n5 15\n10 20",
"output": "2"
},
{
"input": "2\n1 3\n1 6",
"output": "1"
},
{
"input": "2\n1 2\n1 3",
"output": "1"
},
{
"input": "3\n5 6\n1 3\n1 4",
"output": "2"
},
{
"input": "3\n1 4\n2 100\n4 5",
"output": "3"
},
{
"input": "4\n1 1\n3 3\n4 7\n4 5",
"output": "4"
},
{
"input": "3\n2 3\n3 4\n1 2",
"output": "1"
},
{
"input": "1\n0 0",
"output": "-1"
},
{
"input": "6\n99 100\n65 65\n34 34\n16 18\n65 67\n88 88",
"output": "2"
},
{
"input": "2\n50 67\n54 64",
"output": "2"
},
{
"input": "3\n1 3\n2 100\n3 5",
"output": "3"
},
{
"input": "3\n57 90\n35 45\n18 52",
"output": "2"
},
{
"input": "4\n14 15\n46 73\n15 40\n28 53",
"output": "-1"
},
{
"input": "3\n37 38\n51 54\n28 28",
"output": "-1"
},
{
"input": "2\n64 66\n47 61",
"output": "-1"
},
{
"input": "4\n50 68\n63 67\n67 69\n11 12",
"output": "2"
},
{
"input": "4\n42 62\n93 103\n34 62\n5 12",
"output": "1"
},
{
"input": "6\n42 60\n78 107\n6 38\n58 81\n70 105\n70 105",
"output": "5"
},
{
"input": "5\n71 71\n21 22\n58 58\n57 57\n16 16",
"output": "-1"
},
{
"input": "7\n28 42\n70 75\n83 92\n19 22\n26 32\n85 99\n30 39",
"output": "7"
},
{
"input": "3\n8 28\n80 110\n39 81",
"output": "-1"
},
{
"input": "7\n90 115\n87 113\n2 26\n39 40\n91 112\n42 53\n65 79",
"output": "5"
},
{
"input": "7\n12 13\n26 28\n9 11\n15 15\n8 10\n22 24\n5 7",
"output": "-1"
},
{
"input": "7\n3 5\n26 31\n11 15\n2 4\n16 18\n4 4\n7 12",
"output": "6"
},
{
"input": "3\n1 5\n1 2\n4 5",
"output": "2"
},
{
"input": "3\n999999995 999999997\n999999998 1000000000\n999999996 999999999",
"output": "3"
},
{
"input": "4\n1 2\n4 6\n4 10\n200 300",
"output": "2"
}
] | 0 | 0 | -1 | 12,865 |
|
0 | none | [
"none"
] | null | null | A schoolboy named Vasya loves reading books on programming and mathematics. He has recently read an encyclopedia article that described the method of median smoothing (or median filter) and its many applications in science and engineering. Vasya liked the idea of the method very much, and he decided to try it in practice.
Applying the simplest variant of median smoothing to the sequence of numbers *a*1,<=*a*2,<=...,<=*a**n* will result a new sequence *b*1,<=*b*2,<=...,<=*b**n* obtained by the following algorithm:
- *b*1<==<=*a*1, *b**n*<==<=*a**n*, that is, the first and the last number of the new sequence match the corresponding numbers of the original sequence. - For *i*<==<=2,<=...,<=*n*<=-<=1 value *b**i* is equal to the median of three values *a**i*<=-<=1, *a**i* and *a**i*<=+<=1.
The median of a set of three numbers is the number that goes on the second place, when these three numbers are written in the non-decreasing order. For example, the median of the set 5, 1, 2 is number 2, and the median of set 1, 0, 1 is equal to 1.
In order to make the task easier, Vasya decided to apply the method to sequences consisting of zeros and ones only.
Having made the procedure once, Vasya looked at the resulting sequence and thought: what if I apply the algorithm to it once again, and then apply it to the next result, and so on? Vasya tried a couple of examples and found out that after some number of median smoothing algorithm applications the sequence can stop changing. We say that the sequence is stable, if it does not change when the median smoothing is applied to it.
Now Vasya wonders, whether the sequence always eventually becomes stable. He asks you to write a program that, given a sequence of zeros and ones, will determine whether it ever becomes stable. Moreover, if it ever becomes stable, then you should determine what will it look like and how many times one needs to apply the median smoothing algorithm to initial sequence in order to obtain a stable one. | The first input line of the input contains a single integer *n* (3<=≤<=*n*<=≤<=500<=000) — the length of the initial sequence.
The next line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (*a**i*<==<=0 or *a**i*<==<=1), giving the initial sequence itself. | If the sequence will never become stable, print a single number <=-<=1.
Otherwise, first print a single integer — the minimum number of times one needs to apply the median smoothing algorithm to the initial sequence before it becomes is stable. In the second line print *n* numbers separated by a space — the resulting sequence itself. | [
"4\n0 0 1 1\n",
"5\n0 1 0 1 0\n"
] | [
"0\n0 0 1 1\n",
"2\n0 0 0 0 0\n"
] | In the second sample the stabilization occurs in two steps: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5a983e7baab048cbe43812cb997c15e9d7100231.png" style="max-width: 100.0%;max-height: 100.0%;"/>, and the sequence 00000 is obviously stable. | [
{
"input": "4\n0 0 1 1",
"output": "0\n0 0 1 1"
},
{
"input": "5\n0 1 0 1 0",
"output": "2\n0 0 0 0 0"
},
{
"input": "3\n1 0 0",
"output": "0\n1 0 0"
},
{
"input": "4\n1 0 0 1",
"output": "0\n1 0 0 1"
},
{
"input": "7\n1 0 1 1 1 0 1",
"output": "1\n1 1 1 1 1 1 1"
},
{
"input": "14\n0 1 0 0 0 1 1 0 1 0 1 0 1 0",
"output": "3\n0 0 0 0 0 1 1 1 1 1 0 0 0 0"
},
{
"input": "3\n1 0 1",
"output": "1\n1 1 1"
},
{
"input": "3\n0 0 1",
"output": "0\n0 0 1"
},
{
"input": "3\n1 1 0",
"output": "0\n1 1 0"
},
{
"input": "3\n1 1 1",
"output": "0\n1 1 1"
},
{
"input": "4\n1 1 0 1",
"output": "1\n1 1 1 1"
},
{
"input": "4\n1 0 1 1",
"output": "1\n1 1 1 1"
},
{
"input": "10\n0 1 0 1 0 0 1 0 1 0",
"output": "2\n0 0 0 0 0 0 0 0 0 0"
},
{
"input": "4\n0 1 1 0",
"output": "0\n0 1 1 0"
},
{
"input": "168\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0",
"output": "36\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0"
},
{
"input": "3\n0 1 1",
"output": "0\n0 1 1"
},
{
"input": "3\n0 0 0",
"output": "0\n0 0 0"
},
{
"input": "4\n0 1 0 1",
"output": "1\n0 0 1 1"
},
{
"input": "3\n0 1 0",
"output": "1\n0 0 0"
}
] | 62 | 0 | 0 | 12,874 |
|
1,003 | Coins and Queries | [
"greedy"
] | null | null | Polycarp has $n$ coins, the value of the $i$-th coin is $a_i$. It is guaranteed that all the values are integer powers of $2$ (i.e. $a_i = 2^d$ for some non-negative integer number $d$).
Polycarp wants to know answers on $q$ queries. The $j$-th query is described as integer number $b_j$. The answer to the query is the minimum number of coins that is necessary to obtain the value $b_j$ using some subset of coins (Polycarp can use only coins he has). If Polycarp can't obtain the value $b_j$, the answer to the $j$-th query is -1.
The queries are independent (the answer on the query doesn't affect Polycarp's coins). | The first line of the input contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the number of coins and the number of queries.
The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ — values of coins ($1 \le a_i \le 2 \cdot 10^9$). It is guaranteed that all $a_i$ are integer powers of $2$ (i.e. $a_i = 2^d$ for some non-negative integer number $d$).
The next $q$ lines contain one integer each. The $j$-th line contains one integer $b_j$ — the value of the $j$-th query ($1 \le b_j \le 10^9$). | Print $q$ integers $ans_j$. The $j$-th integer must be equal to the answer on the $j$-th query. If Polycarp can't obtain the value $b_j$ the answer to the $j$-th query is -1. | [
"5 4\n2 4 8 2 4\n8\n5\n14\n10\n"
] | [
"1\n-1\n3\n2\n"
] | none | [
{
"input": "5 4\n2 4 8 2 4\n8\n5\n14\n10",
"output": "1\n-1\n3\n2"
},
{
"input": "3 3\n1 1 1\n1\n2\n3",
"output": "1\n2\n3"
},
{
"input": "4 1\n2 4 16 32\n14",
"output": "-1"
},
{
"input": "1 10\n8\n1\n2\n3\n4\n5\n6\n7\n8\n9\n16",
"output": "-1\n-1\n-1\n-1\n-1\n-1\n-1\n1\n-1\n-1"
},
{
"input": "1 10\n4\n1\n2\n3\n4\n5\n6\n7\n8\n9\n16",
"output": "-1\n-1\n-1\n1\n-1\n-1\n-1\n-1\n-1\n-1"
},
{
"input": "1 10\n2\n1\n2\n3\n4\n5\n6\n7\n8\n9\n16",
"output": "-1\n1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1"
},
{
"input": "1 10\n1\n1\n2\n3\n4\n5\n6\n7\n8\n9\n16",
"output": "1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1"
}
] | 2,000 | 13,414,400 | 0 | 12,890 |
|
579 | Finding Team Member | [
"brute force",
"implementation",
"sortings"
] | null | null | There is a programing contest named SnakeUp, 2*n* people want to compete for it. In order to attend this contest, people need to form teams of exactly two people. You are given the strength of each possible combination of two people. All the values of the strengths are distinct.
Every contestant hopes that he can find a teammate so that their team’s strength is as high as possible. That is, a contestant will form a team with highest strength possible by choosing a teammate from ones who are willing to be a teammate with him/her. More formally, two people *A* and *B* may form a team if each of them is the best possible teammate (among the contestants that remain unpaired) for the other one.
Can you determine who will be each person’s teammate? | There are 2*n* lines in the input.
The first line contains an integer *n* (1<=≤<=*n*<=≤<=400) — the number of teams to be formed.
The *i*-th line (*i*<=><=1) contains *i*<=-<=1 numbers *a**i*1, *a**i*2, ... , *a**i*(*i*<=-<=1). Here *a**ij* (1<=≤<=*a**ij*<=≤<=106, all *a**ij* are distinct) denotes the strength of a team consisting of person *i* and person *j* (people are numbered starting from 1.) | Output a line containing 2*n* numbers. The *i*-th number should represent the number of teammate of *i*-th person. | [
"2\n6\n1 2\n3 4 5\n",
"3\n487060\n3831 161856\n845957 794650 976977\n83847 50566 691206 498447\n698377 156232 59015 382455 626960\n"
] | [
"2 1 4 3\n",
"6 5 4 3 2 1\n"
] | In the first sample, contestant 1 and 2 will be teammates and so do contestant 3 and 4, so the teammate of contestant 1, 2, 3, 4 will be 2, 1, 4, 3 respectively. | [
{
"input": "2\n6\n1 2\n3 4 5",
"output": "2 1 4 3"
},
{
"input": "3\n487060\n3831 161856\n845957 794650 976977\n83847 50566 691206 498447\n698377 156232 59015 382455 626960",
"output": "6 5 4 3 2 1"
},
{
"input": "3\n8\n1 6\n14 13 15\n4 2 11 9\n12 5 3 7 10",
"output": "6 5 4 3 2 1"
},
{
"input": "1\n1000000",
"output": "2 1"
},
{
"input": "3\n1000000\n999999 999998\n999997 999996 999995\n999994 999993 999992 999991\n999990 999989 999988 999987 999986",
"output": "2 1 4 3 6 5"
}
] | 327 | 35,840,000 | 3 | 12,915 |
|
812 | Sagheer, the Hausmeister | [
"bitmasks",
"brute force",
"dp"
] | null | null | Some people leave the lights at their workplaces on when they leave that is a waste of resources. As a hausmeister of DHBW, Sagheer waits till all students and professors leave the university building, then goes and turns all the lights off.
The building consists of *n* floors with stairs at the left and the right sides. Each floor has *m* rooms on the same line with a corridor that connects the left and right stairs passing by all the rooms. In other words, the building can be represented as a rectangle with *n* rows and *m*<=+<=2 columns, where the first and the last columns represent the stairs, and the *m* columns in the middle represent rooms.
Sagheer is standing at the ground floor at the left stairs. He wants to turn all the lights off in such a way that he will not go upstairs until all lights in the floor he is standing at are off. Of course, Sagheer must visit a room to turn the light there off. It takes one minute for Sagheer to go to the next floor using stairs or to move from the current room/stairs to a neighboring room/stairs on the same floor. It takes no time for him to switch the light off in the room he is currently standing in. Help Sagheer find the minimum total time to turn off all the lights.
Note that Sagheer does not have to go back to his starting position, and he does not have to visit rooms where the light is already switched off. | The first line contains two integers *n* and *m* (1<=≤<=*n*<=≤<=15 and 1<=≤<=*m*<=≤<=100) — the number of floors and the number of rooms in each floor, respectively.
The next *n* lines contains the building description. Each line contains a binary string of length *m*<=+<=2 representing a floor (the left stairs, then *m* rooms, then the right stairs) where 0 indicates that the light is off and 1 indicates that the light is on. The floors are listed from top to bottom, so that the last line represents the ground floor.
The first and last characters of each string represent the left and the right stairs, respectively, so they are always 0. | Print a single integer — the minimum total time needed to turn off all the lights. | [
"2 2\n0010\n0100\n",
"3 4\n001000\n000010\n000010\n",
"4 3\n01110\n01110\n01110\n01110\n"
] | [
"5\n",
"12\n",
"18\n"
] | In the first example, Sagheer will go to room 1 in the ground floor, then he will go to room 2 in the second floor using the left or right stairs.
In the second example, he will go to the fourth room in the ground floor, use right stairs, go to the fourth room in the second floor, use right stairs again, then go to the second room in the last floor.
In the third example, he will walk through the whole corridor alternating between the left and right stairs at each floor. | [
{
"input": "2 2\n0010\n0100",
"output": "5"
},
{
"input": "3 4\n001000\n000010\n000010",
"output": "12"
},
{
"input": "4 3\n01110\n01110\n01110\n01110",
"output": "18"
},
{
"input": "3 2\n0000\n0100\n0100",
"output": "4"
},
{
"input": "1 89\n0000000000000000000000000000000100000000000000010000000000010000000000000000000000000000000",
"output": "59"
},
{
"input": "2 73\n000000000000000000000000000000000000000000000000000000000000000000000000000\n000000000000000000000000000000000000000100000010000000000000000000000000000",
"output": "46"
},
{
"input": "3 61\n000000000000000000000000000000000000000000000000000000000000000\n000000000000000000000000000000000000000000000000000000000000000\n000000000000000000000000000000000000000000000000000000000000000",
"output": "0"
},
{
"input": "4 53\n0000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000",
"output": "0"
},
{
"input": "5 93\n00000000000000000000000000000000000000000000000000000000100000000000000000000000000000000001010\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n00000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n00000000000000000000000000000010000000000000000000100000000000000000000000000000000000000000000\n00000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000",
"output": "265"
},
{
"input": "6 77\n0000000000000000100000000000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000000000000010000000000000\n0000000000010000000000000000000000000000000000000000000000000000000000000000010\n0000000000000000000001000000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000100000000000000000000000000000",
"output": "311"
},
{
"input": "7 65\n0000000001000000000000000010000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000000000000000\n0000000001000001000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000000000000000\n0000000000000000000000000000000000000000000000000000000000000000000",
"output": "62"
},
{
"input": "8 57\n00000000100000000000000000000000000000000000000000000000000\n00000000000000010000000000000000000000000000000000000000000\n00000000000000000000000000000000000100000000000000000000000\n00000000000000000000000000000000000000000000000000000000000\n00000000000000000000000000000000000100000000000000000000000\n00000000000000000000000000000000000000000000000000000000000\n00000000000010000000000000000000000000000000000000000000000\n00000000000000000000000000000000000000000000000001000000000",
"output": "277"
},
{
"input": "12 13\n000000000000000\n000000000000000\n000000000000000\n000000000000000\n000000000000000\n000000000000000\n010000000000000\n000000000000000\n000000000000000\n000000000000000\n000010000000000\n000000000000000",
"output": "14"
},
{
"input": "13 1\n000\n000\n000\n000\n000\n000\n000\n000\n000\n000\n000\n000\n000",
"output": "0"
},
{
"input": "1 33\n00000100101110001101000000110100010",
"output": "33"
},
{
"input": "2 21\n00100110100010010010010\n01000001111001010000000",
"output": "43"
},
{
"input": "3 5\n0001010\n0100000\n0100000",
"output": "11"
},
{
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"output": "184"
},
{
"input": "5 37\n010100000000000000000110000110010000010\n001101100010110011101000001010101101110\n010000001000100010010100000000001010000\n000000000100101000000101100001000001110\n000010000000000000100001001000011100110",
"output": "193"
},
{
"input": "6 25\n011001000100111010000101000\n000000000010000010001000010\n011001100001100001001001010\n000000100000010000000000110\n010001100001000001000000010\n011000001001010111110000100",
"output": "160"
},
{
"input": "7 61\n010000111100010100001000011010100001000000000011100000100010000\n000010011000001000000100110101010001000000010001100000100100100\n000010001000001000000100001000000100100011001110000111000000100\n000000000101000011010000011000000101000001011001000011101010010\n000010010011000000100000110000001000000101000000101000010000010\n000010010101101100100100100011001011101010000101000010000101010\n000100001100001001000000001000000001011000110010100000000010110",
"output": "436"
},
{
"input": "8 49\n000100100000000111110010011100110100010010000011000\n001000000101111000000001111100010010100000010000000\n000000010000011100001000000000101000110010000100100\n000000000001000110000011101101000000100000101010000\n000000110001000101101000000001000000110001000110000\n000100000000000000100100010011000001111101010100110\n000000001000000010101111000100001100000000010111000\n001000010000110000011100000000100110000010001000000",
"output": "404"
},
{
"input": "9 41\n0011000000000101001101001000000001110000010\n0000110000001010110010110010110010010001000\n0001100010100000000001110100100001101000100\n0001010101111010000000010010001001011111000\n0101000101000011101011000000001100110010000\n0001010000000000000001011000000100010101000\n0000010011000000001000110001000010110001000\n0000100010000110100001000000100010001111100\n0000001110100001000001000110001110000100000",
"output": "385"
},
{
"input": "10 29\n0000000000101001100001001011000\n0001110100000000000000100010000\n0010001001000011000100010001000\n0001000010101000000010100010100\n0111000000000000100100100010100\n0001000100011111000100010100000\n0000000000000001000001001011000\n0000101110000001010001011001110\n0000001000101010011000001100100\n0100010000101011010000000000000",
"output": "299"
},
{
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"output": "55"
},
{
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"output": "65"
},
{
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"output": "63"
},
{
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"output": "22"
},
{
"input": "5 44\n0001010010001111111001111111000010100100000010\n0001111001111001101111011111010110001001111110\n0111111010111111011101100011101010100101110110\n0011010011101011101111001001010110000111111100\n0110100111011100110101110010010011011101100100",
"output": "228"
},
{
"input": "6 36\n01110101111111110101011000011111110010\n00011101100010110111111111110001100100\n00001111110010111111101110101110111110\n00110110011100100111011110000000000010\n01100101101001010001011111100111101100\n00011111111011001000011001011110011110",
"output": "226"
},
{
"input": "7 24\n01111001111001011010010100\n00111011010101000111101000\n01001110110010010110011110\n00000101111011011111111000\n01111111101111001001010010\n01110000111101011111111010\n00000100011100110000110000",
"output": "179"
},
{
"input": "8 8\n0011101110\n0110010100\n0100111110\n0111111100\n0011010100\n0001101110\n0111100000\n0110111000",
"output": "77"
},
{
"input": "9 48\n00011010111110111011111001111111111101001111110010\n01000101000101101101111110111101011100001011010010\n00110111110110101110101110111111011011101111011000\n00110111111100010110110110111001001111011010101110\n01111111100101010011111100100111110011001101110100\n01111011110011111101010101010100001110111111111000\n01110101101101110001000010110100010110101111111100\n00111101001010110010110100000111110101010100001000\n00011011010110011111001100111100100011100110110100",
"output": "448"
},
{
"input": "10 40\n010011001001111011011011101111010001010010\n011000000110000010001011111010100000110000\n011010101001110010110110011111010101101000\n000111111010101111000110011111011011011010\n010110101110001001001111111000110011101010\n010011010100111110010100100111100111011110\n001111101100111111111111001010111010000110\n001111110010101100110100101110001011100110\n010111010010001111110101111111111110111000\n011101101111000100111111111001111100111010",
"output": "418"
},
{
"input": "11 28\n011100111101101001011111001110\n010001111110011101101011001000\n001010011011011010101101101100\n001100011001101011011001110100\n010111110011101110000110111100\n010010001111110000011111010100\n001011111111110011101101111010\n001101101011100100011011001110\n001111110110100110101011000010\n000101101011100001101101100100\n010011101101111011100111110100",
"output": "328"
},
{
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"output": "68"
},
{
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"output": "113"
},
{
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"output": "55"
},
{
"input": "4 4\n011110\n010110\n010110\n011110",
"output": "22"
},
{
"input": "5 89\n0011111111111101110110111111111101111011111011101110111111111111111111111111111111111111110\n0111111111111111111111111101111111111111111111111111111111111111111111111111111111111111110\n0111111111111011111111111111111111101111011111111111111111110110111101111111111111111011010\n0111111111111111011011111111111011111111111111111111111111111111111111111111111110111111010\n0111111101111011111110101011111111110111100100101111111011111111111111011011101111111111110",
"output": "453"
},
{
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"output": "472"
},
{
"input": "7 20\n0111111111111111111100\n0111110111111111111110\n0111111111111111111100\n0111111011111111111110\n0111111111111011101110\n0111101011110111111010\n0111111111111111111010",
"output": "151"
},
{
"input": "8 8\n0111111110\n0111101110\n0111111110\n0111111110\n0111111110\n0110111100\n0101111110\n0110111110",
"output": "78"
},
{
"input": "11 24\n01111111111101111111111110\n01111111111111111111111110\n01110111111111111111111110\n01111111111111111111011110\n01111111111111111110111110\n01111010111111100111101110\n01111111111111010101111100\n01111111111111110111111110\n01011101111111111101111110\n00111111011111111110111110\n01111111101111111101111110",
"output": "284"
},
{
"input": "12 12\n01111111111000\n01101111110110\n01111110111110\n01111111111110\n01111111111010\n01011111110110\n01111111111110\n01101101011110\n01111111111110\n01111101011110\n00111111111110\n01111111011110",
"output": "166"
},
{
"input": "15 28\n011111111101011111111101111110\n011111111111111111111111111110\n011101110111011011101111011110\n011111111011111011110111111110\n011111111110101111111111111110\n011111011111110011111111011010\n011110111111001101111111111110\n011111111110111111111011111110\n011111111111111111111111011110\n011111011111111111111011001010\n011111111101111111111101111110\n011111111110111111101111011110\n010111111111101111111111111110\n011111111111111111011111111110\n011011111111111110110111110110",
"output": "448"
},
{
"input": "2 11\n0100000000000\n0000000010000",
"output": "18"
},
{
"input": "1 100\n010010010011100001101101110111101010000101010001111001001101011110000011101110101000100111111001101110",
"output": "100"
},
{
"input": "15 1\n010\n010\n010\n010\n010\n010\n000\n000\n000\n010\n000\n010\n000\n000\n000",
"output": "29"
},
{
"input": "3 3\n00010\n00000\n00010",
"output": "7"
}
] | 139 | 0 | 0 | 12,932 |
|
457 | Golden System | [
"math",
"meet-in-the-middle"
] | null | null | Piegirl got bored with binary, decimal and other integer based counting systems. Recently she discovered some interesting properties about number , in particular that *q*2<==<=*q*<=+<=1, and she thinks it would make a good base for her new unique system. She called it "golden system". In golden system the number is a non-empty string containing 0's and 1's as digits. The decimal value of expression *a*0*a*1...*a**n* equals to .
Soon Piegirl found out that this system doesn't have same properties that integer base systems do and some operations can not be performed on it. She wasn't able to come up with a fast way of comparing two numbers. She is asking for your help.
Given two numbers written in golden system notation, determine which of them has larger decimal value. | Input consists of two lines — one for each number. Each line contains non-empty string consisting of '0' and '1' characters. The length of each string does not exceed 100000. | Print ">" if the first number is larger, "<" if it is smaller and "=" if they are equal. | [
"1000\n111\n",
"00100\n11\n",
"110\n101\n"
] | [
"<\n",
"=\n",
">\n"
] | In the first example first number equals to <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9c955eec678d6e7dcdc7c94fb203e922d2ad19ad.png" style="max-width: 100.0%;max-height: 100.0%;"/>, while second number is approximately 1.618033988<sup class="upper-index">2</sup> + 1.618033988 + 1 ≈ 5.236, which is clearly a bigger number.
In the second example numbers are equal. Each of them is ≈ 2.618. | [
{
"input": "1000\n111",
"output": "<"
},
{
"input": "00100\n11",
"output": "="
},
{
"input": "110\n101",
"output": ">"
},
{
"input": "0\n0",
"output": "="
},
{
"input": "1\n10",
"output": "<"
},
{
"input": "11\n10",
"output": ">"
},
{
"input": "00111\n10100",
"output": "<"
},
{
"input": "00\n1",
"output": "<"
},
{
"input": "01\n010",
"output": "<"
},
{
"input": "111\n00",
"output": ">"
},
{
"input": "1100\n11",
"output": ">"
},
{
"input": "0110\n001",
"output": ">"
},
{
"input": "1111\n0110",
"output": ">"
},
{
"input": "01010\n0011",
"output": ">"
},
{
"input": "0\n1",
"output": "<"
},
{
"input": "1\n0",
"output": ">"
},
{
"input": "1\n1",
"output": "="
},
{
"input": "010000100010100000100010001000001100100010110000101010000010010011001111101101001\n001011100001110101111001100110001011011100000000100111011010010011010100101011111",
"output": "="
},
{
"input": "11111001000\n1011100100",
"output": ">"
},
{
"input": "1001111010001100001010001010010010100010100011101101110011110101011000010111101100111000110110110010\n01111001101111100111111001110110100101001111010001000000001001001111100101101100001101111111100111101",
"output": "<"
},
{
"input": "1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n0",
"output": ">"
},
{
"input": "100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n1",
"output": ">"
},
{
"input": "1\n100000000000000000000000000000000000000000000000000",
"output": "<"
},
{
"input": "1\n1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"output": "<"
},
{
"input": "11111111111111111111111111111111111111111111111111111111111111111111111111111111\n1111111111111111111111111111111111111111111111111111111111111111111111111111111",
"output": ">"
},
{
"input": "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n100000000000000000000",
"output": ">"
},
{
"input": "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n1011111111111111111111111111011011011001101111111110111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"output": ">"
},
{
"input": "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"output": "<"
},
{
"input": "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n1011111111111111111111111111011011011001101111111110111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"output": ">"
},
{
"input": "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"output": "<"
},
{
"input": "100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n0",
"output": ">"
},
{
"input": "1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n1110",
"output": ">"
},
{
"input": "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n1000",
"output": ">"
},
{
"input": "100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n1000",
"output": ">"
},
{
"input": "1\n1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"output": "<"
},
{
"input": "1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n0",
"output": ">"
},
{
"input": "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n10000",
"output": ">"
},
{
"input": "10000100001000010000100001000010000100001000010000\n1",
"output": ">"
},
{
"input": "101001010101010101010100101010101010101010101001010101010100101010101010100101101010100101010100101010101001010101010101010100101010101010101010101001010101010100101010101010100101101010100101010100101010101001010101010101010100101010101010101010101001010101010100101010101010100101101010100101010100101010\n1",
"output": ">"
},
{
"input": "10100\n01011",
"output": ">"
},
{
"input": "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n01111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"output": "<"
},
{
"input": "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n0000001010101011",
"output": ">"
},
{
"input": "110010010101001001001010100100010101010101011111111111111010101000000000000000000010110111111110101010111111111111111111111111111111111\n1011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"output": ">"
},
{
"input": "1100\n0111",
"output": ">"
},
{
"input": "1111111111111111111111111111111111111111111111111\n0",
"output": ">"
},
{
"input": "1100100101010010010010101001000101010101010111111111111110101010000000000000000000101101111111101010101111111111111111111111111111111\n1011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"output": ">"
},
{
"input": "1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n100000000000000000000",
"output": ">"
},
{
"input": "100001000010000100001000010000100001000010000100001111111111111111111111111111111111111111111111111111111111111111111111\n1",
"output": ">"
},
{
"input": "11111111111111111111111111111111111111111111111111111111111111\n1",
"output": ">"
},
{
"input": "1011\n0100",
"output": ">"
},
{
"input": "100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n011000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
"output": "<"
},
{
"input": "1000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000\n1111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"output": "<"
},
{
"input": "111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111001\n000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011",
"output": ">"
},
{
"input": "1000000000000000000000000\n0101010101010101010101011",
"output": "="
},
{
"input": "1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n1",
"output": ">"
},
{
"input": "101010101010101010101010101010101010101010101010101010101010101010101010\n1000000000000000000000000000000000000000000000000000000000000000000000000",
"output": "<"
},
{
"input": "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n0",
"output": ">"
},
{
"input": "111\n1000",
"output": ">"
},
{
"input": "1000000000000000000000000000000000000000000000000\n000",
"output": ">"
},
{
"input": "11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n10",
"output": ">"
},
{
"input": "111111111111111111111111111111111111111111111111\n11",
"output": ">"
},
{
"input": "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n000",
"output": ">"
},
{
"input": "101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010\n1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"output": ">"
},
{
"input": "100000000000000000000000000000000000000000000000\n0",
"output": ">"
}
] | 1,000 | 1,945,600 | 0 | 12,934 |
|
219 | Special Offer! Super Price 999 Bourles! | [
"implementation"
] | null | null | Polycarpus is an amateur businessman. Recently he was surprised to find out that the market for paper scissors is completely free! Without further ado, Polycarpus decided to start producing and selling such scissors.
Polycaprus calculated that the optimal celling price for such scissors would be *p* bourles. However, he read somewhere that customers are attracted by prices that say something like "Special Offer! Super price 999 bourles!". So Polycarpus decided to lower the price a little if it leads to the desired effect.
Polycarpus agrees to lower the price by no more than *d* bourles so that the number of nines at the end of the resulting price is maximum. If there are several ways to do it, he chooses the maximum possible price.
Note, Polycarpus counts only the trailing nines in a price. | The first line contains two integers *p* and *d* (1<=≤<=*p*<=≤<=1018; 0<=≤<=*d*<=<<=*p*) — the initial price of scissors and the maximum possible price reduction.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier. | Print the required price — the maximum price that ends with the largest number of nines and that is less than *p* by no more than *d*.
The required number shouldn't have leading zeroes. | [
"1029 102\n",
"27191 17\n"
] | [
"999\n",
"27189\n"
] | none | [
{
"input": "1029 102",
"output": "999"
},
{
"input": "27191 17",
"output": "27189"
},
{
"input": "1 0",
"output": "1"
},
{
"input": "9 0",
"output": "9"
},
{
"input": "20 1",
"output": "19"
},
{
"input": "100 23",
"output": "99"
},
{
"input": "10281 1",
"output": "10281"
},
{
"input": "2111 21",
"output": "2099"
},
{
"input": "3021 112",
"output": "2999"
},
{
"input": "1000000000000000000 999999999999999999",
"output": "999999999999999999"
},
{
"input": "29287101 301",
"output": "29286999"
},
{
"input": "302918113 8113",
"output": "302917999"
},
{
"input": "23483247283432 47283432",
"output": "23483239999999"
},
{
"input": "47283432 7283432",
"output": "46999999"
},
{
"input": "7283432 7283431",
"output": "6999999"
},
{
"input": "2304324853947 5853947",
"output": "2304319999999"
},
{
"input": "2485348653485 123483",
"output": "2485348599999"
},
{
"input": "29845435345 34543",
"output": "29845429999"
},
{
"input": "2348723847234234 234829384234",
"output": "2348699999999999"
},
{
"input": "2348723847234234 234829384234",
"output": "2348699999999999"
},
{
"input": "596383801524465437 13997918422040",
"output": "596379999999999999"
},
{
"input": "621306590487786841 47851896849379",
"output": "621299999999999999"
},
{
"input": "990575220328844835 100861359807341",
"output": "990499999999999999"
},
{
"input": "403277728241895842 15097810739041",
"output": "403269999999999999"
},
{
"input": "287854791214303304 98046359947548",
"output": "287799999999999999"
},
{
"input": "847222126505823289 115713658562976",
"output": "847199999999999999"
},
{
"input": "991096248227872657 181679439312637",
"output": "990999999999999999"
},
{
"input": "954402996235787062 354162450334047",
"output": "954399999999999999"
},
{
"input": "220466716596033408 44952575147901",
"output": "220459999999999999"
},
{
"input": "559198116944738707 844709119308273",
"output": "558999999999999999"
},
{
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"output": "363979999999999999"
},
{
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"output": "733489999999999999"
},
{
"input": "757663489894439901 139905688448459",
"output": "757599999999999999"
},
{
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"output": "30527999999999999"
},
{
"input": "534463403123444176 67776394133861",
"output": "534399999999999999"
},
{
"input": "399943891120381720 89545256475298",
"output": "399899999999999999"
},
{
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"output": "696999999999999999"
},
{
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"output": "495769999999999999"
},
{
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"output": "343499999999999999"
},
{
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"output": "393775999999999999"
},
{
"input": "830005749156754342 157633405415940",
"output": "829999999999999999"
},
{
"input": "735716632509713228 109839072010906",
"output": "735699999999999999"
},
{
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{
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{
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{
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{
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{
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{
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{
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{
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] | 278 | 512,000 | -1 | 12,962 |
|
88 | Chord | [
"brute force",
"implementation"
] | A. Chord | 2 | 256 | Vasya studies music.
He has learned lots of interesting stuff. For example, he knows that there are 12 notes: C, C#, D, D#, E, F, F#, G, G#, A, B, H. He also knows that the notes are repeated cyclically: after H goes C again, and before C stands H. We will consider the C note in the row's beginning and the C note after the H similar and we will identify them with each other. The distance between the notes along the musical scale is measured in tones: between two consecutive notes there's exactly one semitone, that is, 0.5 tone. The distance is taken from the lowest tone to the uppest one, that is, the distance between C and E is 4 semitones and between E and C is 8 semitones
Vasya also knows what a chord is. A chord is an unordered set of no less than three notes. However, for now Vasya only works with triads, that is with the chords that consist of exactly three notes. He can already distinguish between two types of triads — major and minor.
Let's define a major triad. Let the triad consist of notes *X*, *Y* and *Z*. If we can order the notes so as the distance along the musical scale between *X* and *Y* equals 4 semitones and the distance between *Y* and *Z* is 3 semitones, then the triad is major. The distance between *X* and *Z*, accordingly, equals 7 semitones.
A minor triad is different in that the distance between *X* and *Y* should be 3 semitones and between *Y* and *Z* — 4 semitones.
For example, the triad "C E G" is major: between C and E are 4 semitones, and between E and G are 3 semitones. And the triplet "C# B F" is minor, because if we order the notes as "B C# F", than between B and C# will be 3 semitones, and between C# and F — 4 semitones.
Help Vasya classify the triad the teacher has given to him. | The only line contains 3 space-separated notes in the above-given notation. | Print "major" if the chord is major, "minor" if it is minor, and "strange" if the teacher gave Vasya some weird chord which is neither major nor minor. Vasya promises you that the answer will always be unambiguous. That is, there are no chords that are both major and minor simultaneously. | [
"C E G\n",
"C# B F\n",
"A B H\n"
] | [
"major\n",
"minor\n",
"strange\n"
] | none | [
{
"input": "C E G",
"output": "major"
},
{
"input": "C# B F",
"output": "minor"
},
{
"input": "A B H",
"output": "strange"
},
{
"input": "G H E",
"output": "minor"
},
{
"input": "D# B G",
"output": "major"
},
{
"input": "D# B F#",
"output": "minor"
},
{
"input": "F H E",
"output": "strange"
},
{
"input": "B F# G",
"output": "strange"
},
{
"input": "F# H C",
"output": "strange"
},
{
"input": "C# F C",
"output": "strange"
},
{
"input": "G# C# E",
"output": "minor"
},
{
"input": "D# H G#",
"output": "minor"
},
{
"input": "C F A",
"output": "major"
},
{
"input": "H E G#",
"output": "major"
},
{
"input": "G D# B",
"output": "major"
},
{
"input": "E C G",
"output": "major"
},
{
"input": "G# C# F",
"output": "major"
},
{
"input": "D# C G#",
"output": "major"
},
{
"input": "C# F B",
"output": "minor"
},
{
"input": "D# C G",
"output": "minor"
},
{
"input": "A D F",
"output": "minor"
},
{
"input": "F# H D",
"output": "minor"
},
{
"input": "D A F",
"output": "minor"
},
{
"input": "D A F#",
"output": "major"
},
{
"input": "C# B F",
"output": "minor"
},
{
"input": "A C F",
"output": "major"
},
{
"input": "D F# H",
"output": "minor"
},
{
"input": "H G# D#",
"output": "minor"
},
{
"input": "A D F#",
"output": "major"
},
{
"input": "H E G#",
"output": "major"
},
{
"input": "D# B F#",
"output": "minor"
},
{
"input": "D# H F#",
"output": "major"
},
{
"input": "A D F#",
"output": "major"
},
{
"input": "B G D#",
"output": "major"
},
{
"input": "E A C#",
"output": "major"
},
{
"input": "D H G",
"output": "major"
},
{
"input": "H D F#",
"output": "minor"
},
{
"input": "G D# C",
"output": "minor"
},
{
"input": "H D G",
"output": "major"
},
{
"input": "E C G",
"output": "major"
},
{
"input": "D# A E",
"output": "strange"
},
{
"input": "A F E",
"output": "strange"
},
{
"input": "C E F",
"output": "strange"
},
{
"input": "A B C",
"output": "strange"
},
{
"input": "E F D#",
"output": "strange"
},
{
"input": "C G# G#",
"output": "strange"
},
{
"input": "F D# G#",
"output": "strange"
},
{
"input": "B G D#",
"output": "major"
},
{
"input": "E E G#",
"output": "strange"
},
{
"input": "A G H",
"output": "strange"
},
{
"input": "F E A",
"output": "strange"
},
{
"input": "D B E",
"output": "strange"
},
{
"input": "G# C# D",
"output": "strange"
},
{
"input": "D# D# F#",
"output": "strange"
},
{
"input": "H B G",
"output": "strange"
},
{
"input": "D C B",
"output": "strange"
},
{
"input": "D B B",
"output": "strange"
},
{
"input": "C A H",
"output": "strange"
},
{
"input": "F# H F#",
"output": "strange"
},
{
"input": "A F F#",
"output": "strange"
},
{
"input": "C D C",
"output": "strange"
},
{
"input": "G F# A",
"output": "strange"
},
{
"input": "C C# D",
"output": "strange"
},
{
"input": "C A E",
"output": "minor"
},
{
"input": "A H B",
"output": "strange"
},
{
"input": "B E F#",
"output": "strange"
},
{
"input": "G# G# A",
"output": "strange"
},
{
"input": "B C# C#",
"output": "strange"
},
{
"input": "C G D#",
"output": "minor"
},
{
"input": "C B D#",
"output": "strange"
},
{
"input": "F H F",
"output": "strange"
},
{
"input": "E G# C",
"output": "strange"
},
{
"input": "F# F# F#",
"output": "strange"
},
{
"input": "F C F",
"output": "strange"
},
{
"input": "A F D",
"output": "minor"
}
] | 310 | 0 | 3.9225 | 12,972 |
958 | Guard Duty (easy) | [
"brute force",
"geometry",
"greedy",
"math"
] | null | null | The Rebel fleet is afraid that the Empire might want to strike back again. Princess Heidi needs to know if it is possible to assign *R* Rebel spaceships to guard *B* bases so that every base has exactly one guardian and each spaceship has exactly one assigned base (in other words, the assignment is a perfect matching). Since she knows how reckless her pilots are, she wants to be sure that any two (straight) paths – from a base to its assigned spaceship – do not intersect in the galaxy plane (that is, in 2D), and so there is no risk of collision. | The first line contains two space-separated integers *R*,<=*B*(1<=≤<=*R*,<=*B*<=≤<=10). For 1<=≤<=*i*<=≤<=*R*, the *i*<=+<=1-th line contains two space-separated integers *x**i* and *y**i* (|*x**i*|,<=|*y**i*|<=≤<=10000) denoting the coordinates of the *i*-th Rebel spaceship. The following *B* lines have the same format, denoting the position of bases. It is guaranteed that no two points coincide and that no three points are on the same line. | If it is possible to connect Rebel spaceships and bases so as satisfy the constraint, output Yes, otherwise output No (without quote). | [
"3 3\n0 0\n2 0\n3 1\n-2 1\n0 3\n2 2\n",
"2 1\n1 0\n2 2\n3 1\n"
] | [
"Yes\n",
"No\n"
] | For the first example, one possible way is to connect the Rebels and bases in order.
For the second example, there is no perfect matching between Rebels and bases. | [
{
"input": "3 3\n0 0\n2 0\n3 1\n-2 1\n0 3\n2 2",
"output": "Yes"
},
{
"input": "2 1\n1 0\n2 2\n3 1",
"output": "No"
},
{
"input": "1 1\n3686 4362\n-7485 5112",
"output": "Yes"
},
{
"input": "1 2\n1152 -7324\n-5137 -35\n-6045 -5271",
"output": "No"
},
{
"input": "1 3\n-8824 -9306\n-5646 -9767\n8123 9355\n-6203 -1643",
"output": "No"
},
{
"input": "1 5\n-8775 6730\n-3806 -6906\n-9256 -8240\n-1320 6849\n8155 746\n8284 -7317",
"output": "No"
},
{
"input": "1 8\n8741 3638\n381 -9191\n7534 8792\n-8848 -414\n2926 -7444\n9475 559\n6938 2359\n2570 4721\n3329 -9365",
"output": "No"
},
{
"input": "1 9\n6207 1655\n2728 8520\n9142 3418\n-1258 -8727\n5370 3161\n-5167 -7691\n517 2242\n3702 -9904\n-6862 -2997\n2524 -5492",
"output": "No"
},
{
"input": "1 10\n9424 3979\n-8582 9252\n-2432 -3287\n-4247 1932\n-9491 5544\n-635 5689\n8260 -6790\n8841 3067\n-5624 -1990\n1569 1045\n-8844 -8462",
"output": "No"
},
{
"input": "2 1\n2893 -5488\n-5087 -5042\n-8928 -9453",
"output": "No"
},
{
"input": "2 2\n359 -29\n6964 -7332\n2384 -4529\n4434 2253",
"output": "Yes"
},
{
"input": "2 3\n-9617 845\n4195 -2181\n-6305 -9903\n-535 -6060\n9417 -8419",
"output": "No"
},
{
"input": "2 5\n-9568 -3121\n-1408 2942\n-827 -7497\n4348 2432\n-7958 231\n6440 1896\n2647 -1305",
"output": "No"
},
{
"input": "2 8\n7948 3490\n2779 3512\n3403 -3024\n-3180 -4831\n6815 4601\n7631 9772\n-6320 -1060\n5592 362\n-785 4040\n8030 3272",
"output": "No"
},
{
"input": "2 9\n5414 -8195\n-5171 -1634\n5012 4161\n-5888 -585\n9258 2646\n5548 1523\n7259 -8619\n9580 5738\n-8715 706\n-2232 -3280\n1866 1775",
"output": "No"
},
{
"input": "2 10\n-5118 -3971\n-1169 -9140\n-7807 -3139\n9702 -5328\n8555 3460\n-1442 -733\n701 -2802\n-5784 2578\n8186 -4810\n-2722 -1013\n-9437 4021\n-5403 -1331",
"output": "No"
},
{
"input": "3 1\n-8199 -7896\n7015 -4898\n-499 -8710\n9953 -6411",
"output": "No"
},
{
"input": "3 2\n9268 -9879\n4245 2515\n-9188 -3786\n-2458 -2165\n3420 463",
"output": "No"
},
{
"input": "3 3\n-8149 697\n6593 7667\n2123 -9160\n-5165 9523\n747 -8933\n-1536 -2691",
"output": "Yes"
},
{
"input": "3 5\n-658 7030\n990 3086\n-4958 -6755\n7159 -1986\n5634 -7726\n1740 -1450\n1947 7835\n-2755 -4709",
"output": "No"
},
{
"input": "3 8\n-3143 -6360\n-5121 -6641\n-727 -9723\n-369 454\n-9298 4086\n5787 -1016\n2683 -9660\n-1089 1121\n-4898 7743\n418 5485\n7425 -6644",
"output": "No"
},
{
"input": "3 9\n6882 -8342\n4669 -8932\n882 4904\n-220 4700\n587 -5311\n3704 -1823\n6559 -6921\n-7399 6497\n-5387 -5890\n-9844 -1067\n5367 -7237\n-8314 -939",
"output": "No"
},
{
"input": "3 10\n-7100 -1623\n-3459 2172\n9676 1595\n-6053 4558\n-842 8819\n-9691 3144\n3440 -9112\n7034 4946\n4851 -2513\n430 4372\n-7175 -3497\n5719 381\n-8859 -1347",
"output": "No"
},
{
"input": "5 1\n9621 -154\n6694 -2348\n944 -7225\n-1568 -5543\n-3805 -872\n1204 -2651",
"output": "No"
},
{
"input": "5 2\n-355 -9579\n-1256 -4638\n-4890 7402\n-1420 -1297\n-1362 2290\n-879 9101\n9514 -6689",
"output": "No"
},
{
"input": "5 3\n9670 8440\n1091 -9784\n6422 4884\n3314 -9610\n8523 -7107\n-2963 8293\n3092 -3950\n-4093 -6502",
"output": "No"
},
{
"input": "5 5\n-2840 4475\n2931 -6923\n-659 -8125\n8197 -1118\n851 -5899\n313 6679\n-9751 6115\n-6415 4250\n-227 -9732\n-6282 5041",
"output": "Yes"
},
{
"input": "5 8\n-5325 1383\n-5441 3351\n-3870 1465\n669 -8381\n-4377 5913\n4360 -329\n8725 8620\n7810 -2479\n4019 4850\n8052 9911\n4130 -4668\n3744 2537\n-7171 -3933",
"output": "No"
},
{
"input": "5 9\n-2742 -600\n6609 8502\n-5118 6389\n-4300 5568\n-1934 -3484\n9719 -1137\n2303 -8641\n1500 2897\n-6172 -8783\n-2210 -6939\n9514 -5262\n-3773 -4081\n1983 -4032\n4503 -3496",
"output": "No"
},
{
"input": "5 10\n1493 7658\n-598 7650\n9226 -964\n2439 -3114\n366 2391\n-1008 -2258\n6063 8568\n7488 6824\n-4674 9523\n9590 9960\n-8361 -8234\n520 -1312\n-3878 -1142\n-8261 -239\n-2346 -2362",
"output": "No"
},
{
"input": "8 1\n-796 -1\n3591 -2510\n-6330 4706\n-7422 -9093\n7860 -7002\n5375 -5310\n3538 3108\n-9851 -9798\n-8884 -170",
"output": "No"
},
{
"input": "8 2\n-3330 -1983\n-6621 -4800\n-4721 9630\n9871 -4847\n-2256 -8957\n3292 -6118\n4558 -6712\n-5863 5282\n-9373 3938\n-5179 -8073",
"output": "No"
},
{
"input": "8 3\n6695 8593\n-7129 352\n6590 -5447\n-2540 -3457\n7630 1647\n8651 5634\n-1864 -6829\n7828 -1901\n-7005 -9695\n4561 -4921\n-4782 -6478",
"output": "No"
},
{
"input": "8 5\n6744 2367\n-5290 -7085\n-491 6662\n2343 -2407\n-43 2855\n-8075 6875\n-7265 -4206\n-4197 8851\n7433 780\n4038 -8321\n-1455 -7665\n3139 -1225\n9884 -167",
"output": "No"
},
{
"input": "8 8\n4260 1536\n-8545 6045\n-3702 3693\n-5185 -2228\n-5271 -5335\n-4027 4453\n-8790 8598\n7172 -5320\n-880 -4638\n-1630 -3452\n2076 8296\n-9116 -5599\n2461 9832\n4268 5116\n-7582 -805\n3548 3776",
"output": "Yes"
},
{
"input": "8 9\n-5716 6995\n1245 3754\n7610 8617\n-451 -5424\n-2828 5270\n-6111 6502\n-2653 1039\n3718 7498\n-8810 -7973\n667 -300\n-2838 -2001\n3367 5523\n-8386 -2827\n6929 -6260\n3247 1167\n1873 6265\n4376 -8781",
"output": "No"
},
{
"input": "8 10\n5844 -8156\n9676 -8121\n-6302 -1050\n-4823 -8343\n4736 -3859\n9129 5920\n-3990 2792\n3615 -8930\n-7831 -8703\n-5542 931\n7599 -7930\n8705 -8735\n-6438 1724\n-7568 -8351\n5893 2316\n2574 -9723\n2416 3827\n856 -4877",
"output": "No"
},
{
"input": "9 1\n8114 -9851\n872 -9807\n9541 5449\n7948 -3808\n8892 -7517\n-6767 3903\n-18 -311\n-3973 5845\n-3295 3533\n-4790 -4426",
"output": "No"
},
{
"input": "9 2\n5580 8167\n-7078 -4655\n3707 -9628\n2980 438\n1632 -9472\n-8850 -4346\n-6440 2428\n-2841 923\n6515 -2658\n-2492 -8716\n8219 5104",
"output": "No"
},
{
"input": "9 3\n8163 6185\n-4731 2757\n-4982 -4704\n3128 4684\n-8483 1132\n6807 2288\n4878 2311\n-6295 6299\n8882 -5992\n-195 4733\n6162 4510\n-7264 -1020",
"output": "No"
},
{
"input": "9 5\n-4347 -5222\n-2891 5618\n-4621 7404\n-4548 -6825\n3846 2340\n2640 3530\n-7965 4934\n-8617 -2950\n-9240 4483\n-718 6451\n-8251 -6379\n558 3484\n9861 -6432\n483 -7331",
"output": "No"
},
{
"input": "9 8\n-6832 -872\n1295 -4109\n-7832 -8123\n-2373 -6646\n-1383 -5849\n3832 -6334\n-7229 -2263\n-6951 -9678\n4709 1326\n-6386 -1239\n2721 -8159\n-4255 -890\n9880 3567\n3349 5921\n2487 -828\n-783 2422\n-5497 -8399",
"output": "No"
},
{
"input": "9 9\n3193 -2855\n787 -6399\n3479 9360\n5217 -9842\n1061 4755\n1748 -7142\n-6209 -2380\n6740 -4302\n-5482 5433\n3353 -5529\n664 1546\n8228 -9769\n-8409 -1650\n893 9365\n-9542 8585\n7245 -9972\n-475 -6359\n-3775 2139",
"output": "Yes"
},
{
"input": "9 10\n-3581 3894\n7385 3191\n-8820 6540\n-577 -5900\n2781 -5943\n8322 -7944\n-1251 -5779\n-3567 3140\n8835 -6406\n-2390 -1126\n7006 4553\n-174 -7023\n-6538 1530\n3318 2477\n7864 -9657\n-2379 -6961\n4456 9852\n1462 -5871\n-9931 6466",
"output": "No"
},
{
"input": "10 1\n3362 3137\n-6006 -2168\n-9207 8006\n-6284 -114\n4617 -4997\n-4360 3540\n-6423 2328\n-8768 8468\n2899 1032\n-7561 -3623\n6979 653",
"output": "No"
},
{
"input": "10 2\n5945 8596\n-3658 -4459\n-7598 -7071\n3567 4132\n7060 -1835\n-6443 -4709\n4895 2211\n-4780 3546\n5266 7400\n2178 -472\n4922 -9643\n4163 6030",
"output": "No"
},
{
"input": "10 3\n3411 6614\n8392 693\n-8846 7555\n-1402 -4181\n-3055 -3789\n4033 -5516\n-1527 4950\n-792 8922\n-4925 4065\n4475 5536\n-9695 9764\n6943 -2849\n7022 1986",
"output": "No"
},
{
"input": "10 5\n3460 5504\n529 -6744\n4075 9961\n-3961 4311\n-7871 9977\n7308 -4275\n-6928 7573\n-3114 -327\n-3046 -5461\n3953 4398\n-4106 -3981\n-8092 -8048\n7590 9228\n9433 -4\n-8808 -6742",
"output": "No"
},
{
"input": "10 8\n8417 -444\n-5582 6386\n863 6992\n-4047 6751\n-5658 1788\n-1204 5862\n-6192 -2480\n813 -7056\n-9098 -1176\n-1715 -3292\n6866 -2905\n-7788 137\n7609 -774\n-7702 -6753\n-6622 -3090\n3089 -7006\n-9374 1882\n-481 -5698",
"output": "No"
},
{
"input": "10 9\n-9001 -9868\n4207 1240\n-7826 1618\n-6755 3555\n-3214 -167\n4155 -4648\n-2316 259\n4801 -1679\n-6730 8048\n-4535 -9843\n4809 -5759\n4695 -8742\n9321 -5991\n2401 4133\n6468 6324\n1414 -9103\n-6613 3922\n5544 -5092\n-6777 -788",
"output": "No"
},
{
"input": "10 10\n8530 -3814\n-9330 -6035\n3951 -217\n-9276 8291\n636 -3118\n5024 -2403\n4601 7977\n-3620 -1428\n4954 -9632\n-9852 6553\n-3457 5430\n-8866 -7343\n1020 -5748\n5043 -3820\n-2832 1528\n-5058 -825\n2406 -3530\n9152 -7463\n-8547 7108\n2492 8953",
"output": "Yes"
}
] | 46 | 0 | 0 | 12,994 |
|
107 | Dorm Water Supply | [
"dfs and similar",
"graphs"
] | A. Dorm Water Supply | 1 | 256 | The German University in Cairo (GUC) dorm houses are numbered from 1 to *n*. Underground water pipes connect these houses together. Each pipe has certain direction (water can flow only in this direction and not vice versa), and diameter (which characterizes the maximal amount of water it can handle).
For each house, there is at most one pipe going into it and at most one pipe going out of it. With the new semester starting, GUC student and dorm resident, Lulu, wants to install tanks and taps at the dorms. For every house with an outgoing water pipe and without an incoming water pipe, Lulu should install a water tank at that house. For every house with an incoming water pipe and without an outgoing water pipe, Lulu should install a water tap at that house. Each tank house will convey water to all houses that have a sequence of pipes from the tank to it. Accordingly, each tap house will receive water originating from some tank house.
In order to avoid pipes from bursting one week later (like what happened last semester), Lulu also has to consider the diameter of the pipes. The amount of water each tank conveys should not exceed the diameter of the pipes connecting a tank to its corresponding tap. Lulu wants to find the maximal amount of water that can be safely conveyed from each tank to its corresponding tap. | The first line contains two space-separated integers *n* and *p* (1<=≤<=*n*<=≤<=1000,<=0<=≤<=*p*<=≤<=*n*) — the number of houses and the number of pipes correspondingly.
Then *p* lines follow — the description of *p* pipes. The *i*-th line contains three integers *a**i* *b**i* *d**i*, indicating a pipe of diameter *d**i* going from house *a**i* to house *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*,<=*a**i*<=≠<=*b**i*,<=1<=≤<=*d**i*<=≤<=106).
It is guaranteed that for each house there is at most one pipe going into it and at most one pipe going out of it. | Print integer *t* in the first line — the number of tank-tap pairs of houses.
For the next *t* lines, print 3 integers per line, separated by spaces: *tank**i*, *tap**i*, and *diameter**i*, where *tank**i*<=≠<=*tap**i* (1<=≤<=*i*<=≤<=*t*). Here *tank**i* and *tap**i* are indexes of tank and tap houses respectively, and *diameter**i* is the maximum amount of water that can be conveyed. All the *t* lines should be ordered (increasingly) by *tank**i*. | [
"3 2\n1 2 10\n2 3 20\n",
"3 3\n1 2 20\n2 3 10\n3 1 5\n",
"4 2\n1 2 60\n3 4 50\n"
] | [
"1\n1 3 10\n",
"0\n",
"2\n1 2 60\n3 4 50\n"
] | none | [
{
"input": "3 2\n1 2 10\n2 3 20",
"output": "1\n1 3 10"
},
{
"input": "3 3\n1 2 20\n2 3 10\n3 1 5",
"output": "0"
},
{
"input": "4 2\n1 2 60\n3 4 50",
"output": "2\n1 2 60\n3 4 50"
},
{
"input": "10 10\n10 3 70\n1 9 98\n9 10 67\n5 2 78\n8 6 71\n4 8 95\n7 1 10\n2 5 73\n6 7 94\n3 4 23",
"output": "0"
},
{
"input": "7 5\n3 2 26\n4 6 84\n6 3 82\n5 1 57\n1 7 34",
"output": "2\n4 2 26\n5 7 34"
},
{
"input": "9 6\n7 4 98\n5 9 72\n4 6 10\n2 8 22\n9 7 17\n3 1 66",
"output": "3\n2 8 22\n3 1 66\n5 6 10"
},
{
"input": "8 6\n1 3 84\n8 4 34\n7 2 10\n6 8 8\n3 5 39\n2 7 8",
"output": "2\n1 5 39\n6 4 8"
},
{
"input": "10 8\n2 3 49\n4 8 26\n5 2 76\n3 5 94\n1 7 16\n10 9 77\n6 4 24\n7 1 7",
"output": "2\n6 8 24\n10 9 77"
},
{
"input": "6 5\n2 6 47\n3 4 27\n5 2 47\n4 1 62\n1 5 61",
"output": "1\n3 6 27"
},
{
"input": "5 4\n5 2 9\n4 1 94\n3 5 82\n2 3 58",
"output": "1\n4 1 94"
},
{
"input": "1000 0",
"output": "0"
},
{
"input": "2 2\n1 2 1\n2 1 1",
"output": "0"
},
{
"input": "44 42\n4 37 166\n34 25 47\n28 19 367\n20 14 811\n8 3 878\n39 1 925\n35 9 206\n32 18 841\n16 44 503\n5 20 426\n22 34 896\n44 43 471\n17 33 577\n40 22 317\n24 31 818\n37 11 292\n21 39 888\n6 8 983\n43 36 170\n11 21 662\n36 17 942\n18 7 356\n2 32 220\n12 5 774\n19 27 193\n13 40 63\n15 10 510\n30 35 869\n41 24 736\n42 4 180\n23 41 261\n9 28 501\n29 15 983\n10 30 638\n7 13 402\n26 12 754\n25 6 597\n27 29 57\n1 16 933\n31 42 135\n33 38 718\n14 23 361",
"output": "2\n2 3 47\n26 38 135"
},
{
"input": "35 33\n22 7 978\n5 6 566\n20 10 198\n6 17 170\n7 27 627\n24 19 659\n31 30 130\n34 8 365\n23 12 716\n4 29 217\n8 20 156\n26 35 142\n3 2 419\n15 1 448\n17 24 91\n18 33 962\n30 22 822\n9 16 847\n2 9 470\n10 25 981\n16 31 359\n19 28 283\n28 34 199\n11 5 660\n25 23 176\n29 18 235\n12 14 765\n14 11 81\n27 21 61\n21 13 651\n35 3 583\n1 32 767\n13 4 256",
"output": "2\n15 32 448\n26 33 61"
},
{
"input": "33 28\n12 15 574\n11 13 714\n13 33 62\n9 28 391\n22 19 235\n6 20 655\n23 9 25\n8 29 994\n21 30 133\n17 18 170\n32 7 470\n14 21 418\n7 31 431\n3 1 185\n1 14 538\n33 12 250\n31 22 694\n2 27 945\n16 26 584\n19 32 317\n27 2 904\n15 25 748\n29 3 754\n24 4 287\n18 10 775\n30 11 401\n10 8 653\n28 5 70",
"output": "5\n6 20 655\n16 26 584\n17 25 62\n23 5 25\n24 4 287"
},
{
"input": "3 1\n1 2 10",
"output": "1\n1 2 10"
},
{
"input": "1 0",
"output": "0"
},
{
"input": "2 0",
"output": "0"
},
{
"input": "3 0",
"output": "0"
}
] | 264 | 30,208,000 | 0 | 13,007 |
555 | Case of Computer Network | [
"dfs and similar",
"graphs",
"trees"
] | null | null | Andrewid the Android is a galaxy-known detective. Now he is preparing a defense against a possible attack by hackers on a major computer network.
In this network are *n* vertices, some pairs of vertices are connected by *m* undirected channels. It is planned to transfer *q* important messages via this network, the *i*-th of which must be sent from vertex *s**i* to vertex *d**i* via one or more channels, perhaps through some intermediate vertices.
To protect against attacks a special algorithm was developed. Unfortunately it can be applied only to the network containing directed channels. Therefore, as new channels can't be created, it was decided for each of the existing undirected channels to enable them to transmit data only in one of the two directions.
Your task is to determine whether it is possible so to choose the direction for each channel so that each of the *q* messages could be successfully transmitted. | The first line contains three integers *n*, *m* and *q* (1<=≤<=*n*,<=*m*,<=*q*<=≤<=2·105) — the number of nodes, channels and important messages.
Next *m* lines contain two integers each, *v**i* and *u**i* (1<=≤<=*v**i*,<=*u**i*<=≤<=*n*, *v**i*<=≠<=*u**i*), that means that between nodes *v**i* and *u**i* is a channel. Between a pair of nodes can exist more than one channel.
Next *q* lines contain two integers *s**i* and *d**i* (1<=≤<=*s**i*,<=*d**i*<=≤<=*n*, *s**i*<=≠<=*d**i*) — the numbers of the nodes of the source and destination of the corresponding message.
It is not guaranteed that in it initially possible to transmit all the messages. | If a solution exists, print on a single line "Yes" (without the quotes). Otherwise, print "No" (without the quotes). | [
"4 4 2\n1 2\n1 3\n2 3\n3 4\n1 3\n4 2\n",
"3 2 2\n1 2\n3 2\n1 3\n2 1\n",
"3 3 2\n1 2\n1 2\n3 2\n1 3\n2 1\n"
] | [
"Yes\n",
"No\n",
"Yes\n"
] | In the first sample test you can assign directions, for example, as follows: 1 → 2, 1 → 3, 3 → 2, 4 → 3. Then the path for for the first message will be 1 → 3, and for the second one — 4 → 3 → 2.
In the third sample test you can assign directions, for example, as follows: 1 → 2, 2 → 1, 2 → 3. Then the path for the first message will be 1 → 2 → 3, and for the second one — 2 → 1. | [] | 0 | 0 | -1 | 13,087 |
|
549 | Degenerate Matrix | [
"binary search",
"math"
] | null | null | The determinant of a matrix 2<=×<=2 is defined as follows:
A matrix is called degenerate if its determinant is equal to zero.
The norm ||*A*|| of a matrix *A* is defined as a maximum of absolute values of its elements.
You are given a matrix . Consider any degenerate matrix *B* such that norm ||*A*<=-<=*B*|| is minimum possible. Determine ||*A*<=-<=*B*||. | The first line contains two integers *a* and *b* (|*a*|,<=|*b*|<=≤<=109), the elements of the first row of matrix *A*.
The second line contains two integers *c* and *d* (|*c*|,<=|*d*|<=≤<=109) the elements of the second row of matrix *A*. | Output a single real number, the minimum possible value of ||*A*<=-<=*B*||. Your answer is considered to be correct if its absolute or relative error does not exceed 10<=-<=9. | [
"1 2\n3 4\n",
"1 0\n0 1\n"
] | [
"0.2000000000\n",
"0.5000000000\n"
] | In the first sample matrix *B* is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ce214ad27bde5d77f87492eedd74d34c745f72a1.png" style="max-width: 100.0%;max-height: 100.0%;"/>
In the second sample matrix *B* is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/a07c34fbc6e9328bcb519d3f780eea6e02e5dc87.png" style="max-width: 100.0%;max-height: 100.0%;"/> | [
{
"input": "1 2\n3 4",
"output": "0.2000000000"
},
{
"input": "1 0\n0 1",
"output": "0.5000000000"
},
{
"input": "1000000000 0\n0 1000000000",
"output": "500000000.0000000000"
},
{
"input": "8205 9482\n11 -63",
"output": "35.0198432832"
},
{
"input": "0 0\n0 0",
"output": "0.0000000000"
},
{
"input": "1000000000 -1000000000\n1000000000 1000000000",
"output": "1000000000.0000000000"
},
{
"input": "1000000000 1000000000\n1000000000 -1000000000",
"output": "1000000000.0000000000"
},
{
"input": "-1 -1\n1 0",
"output": "0.3333333333"
},
{
"input": "5 2\n-15 -6",
"output": "0.0000000000"
},
{
"input": "2 -5\n-3 2",
"output": "0.9166666667"
},
{
"input": "-5 -2\n-1 -3",
"output": "1.1818181818"
},
{
"input": "-5 8\n1 6",
"output": "2.1111111111"
},
{
"input": "1 3\n3 2",
"output": "0.7777777778"
},
{
"input": "-42 63\n77 -32",
"output": "16.3878504673"
},
{
"input": "91 -7\n-21 91",
"output": "38.7333333333"
},
{
"input": "-67 -77\n-56 -75",
"output": "2.5927272727"
},
{
"input": "-26 53\n-48 -89",
"output": "29.6219512195"
},
{
"input": "97 -934\n-707 184",
"output": "334.2819979188"
},
{
"input": "689 412\n-794 -421",
"output": "16.0012953368"
},
{
"input": "-718 -387\n972 972",
"output": "105.5204985241"
},
{
"input": "-126 -376\n75 367",
"output": "19.1122881356"
},
{
"input": "-7 -3674\n845 5737",
"output": "298.5843320666"
},
{
"input": "-9912 755\n-8220 6419",
"output": "2268.9886983324"
},
{
"input": "-3928 5185\n4331 6665",
"output": "3969.3426099731"
},
{
"input": "2056 9614\n-5171 8965",
"output": "3141.2387756983"
},
{
"input": "41642 63236\n-59604 20357",
"output": "32033.4760659150"
},
{
"input": "-38387 -93294\n-52918 -51288",
"output": "12582.8868737997"
},
{
"input": "92812 73253\n-46231 11374",
"output": "22109.0927374802"
},
{
"input": "12784 -94506\n26149 85264",
"output": "18439.1869417765"
},
{
"input": "955162 -709099\n-743655 578837",
"output": "8557.1487662354"
},
{
"input": "160382 -103968\n301943 -156088",
"output": "8802.4244934460"
},
{
"input": "-634398 -468280\n447621 78431",
"output": "98147.3248125840"
},
{
"input": "-398622 -832591\n-506781 -656493",
"output": "66924.0413186624"
},
{
"input": "-2665612 -7693032\n-2861368 -6201836",
"output": "282203.1726406262"
},
{
"input": "1762462 700391\n-7134185 5042962",
"output": "1048758.9114990780"
},
{
"input": "6190536 5693104\n-8006293 -3712238",
"output": "957535.4624752104"
},
{
"input": "553632 5653328\n-7246622 9164341",
"output": "2140390.1895580233"
},
{
"input": "43469186 94408326\n78066381 -19616812",
"output": "41883387.4306073852"
},
{
"input": "25683826 49101909\n88380777 46573745",
"output": "14987456.1603828062"
},
{
"input": "-87068851 98762810\n3727856 -87235696",
"output": "26110777.7289122988"
},
{
"input": "95145788 53456393\n42406028 83987544",
"output": "20815549.6776987243"
},
{
"input": "876432079 -414820618\n-816514132 -914565422",
"output": "520028295.4718751899"
},
{
"input": "-240038673 376842703\n-241080203 410087456",
"output": "5983627.7655281517"
},
{
"input": "938457872 -536526676\n867891897 -855194260",
"output": "105349963.0995401485"
},
{
"input": "116954418 255136645\n-851641472 174491320",
"output": "204147910.8375163887"
},
{
"input": "1 1\n1 5",
"output": "0.5000000000"
},
{
"input": "1 5\n1 1",
"output": "0.5000000000"
},
{
"input": "5 1\n1 1",
"output": "0.5000000000"
},
{
"input": "1 1\n5 1",
"output": "0.5000000000"
},
{
"input": "-1000000000 -1000000000\n1000000000 1000000000",
"output": "0.0000000000"
},
{
"input": "-1000000000 -1000000000\n999999999 999999999",
"output": "0.0000000000"
},
{
"input": "536870912 88\n536870912 22528",
"output": "11219.7636804586"
},
{
"input": "268435456 268435456\n22512 22528",
"output": "7.9993289080"
},
{
"input": "-1 1\n1 1",
"output": "1.0000000000"
},
{
"input": "-1000 -999\n-1 0",
"output": "0.4995000000"
},
{
"input": "-801658422 -738703776\n910442649 -920729415",
"output": "744753719.5468964978"
},
{
"input": "-203893419 -777818\n295920256 -474540430",
"output": "99618123.5339717944"
},
{
"input": "448944609 529185527\n946362390 958011342",
"output": "24529803.2444389601"
},
{
"input": "348741875 -606207234\n-279810821 -14278204",
"output": "143060520.9047362779"
},
{
"input": "-202195424 182466434\n-722509868 -838173079",
"output": "190651913.7089770083"
},
{
"input": "-48 9\n17 -67",
"output": "21.7234042553"
},
{
"input": "12 180\n79 47",
"output": "42.9433962264"
},
{
"input": "-131 -87\n-66 -109",
"output": "21.7226463104"
},
{
"input": "171 17\n9 93",
"output": "54.3103448276"
},
{
"input": "221 20\n-22 -200",
"output": "94.5140388769"
},
{
"input": "372 -352\n-160 -423",
"output": "216.4903748734"
},
{
"input": "480 37\n-3 -459",
"output": "224.9325842697"
},
{
"input": "-535 -395\n-264 513",
"output": "321.2340966921"
},
{
"input": "-498 -685\n-532 526",
"output": "503.1068273092"
},
{
"input": "-16 450\n-848 27",
"output": "284.2416107383"
},
{
"input": "-621967643 610314360\n-660274542 -772630232",
"output": "611623765.8647500770"
},
{
"input": "222416863 97256131\n897661932 -426944193",
"output": "125718637.9005708302"
},
{
"input": "67861199 302935298\n883117733 559626116",
"output": "126575973.2879779836"
},
{
"input": "1000000000 1\n1000000000 2",
"output": "0.4999999993"
},
{
"input": "-2 1\n1 -2",
"output": "0.5000000000"
},
{
"input": "1000000000 999999995\n99999999 -199992543",
"output": "142854098.7306812546"
}
] | 156 | 5,632,000 | 3 | 13,105 |
|
673 | Problems for Round | [
"greedy",
"implementation"
] | null | null | There are *n* problems prepared for the next Codeforces round. They are arranged in ascending order by their difficulty, and no two problems have the same difficulty. Moreover, there are *m* pairs of similar problems. Authors want to split problems between two division according to the following rules:
- Problemset of each division should be non-empty. - Each problem should be used in exactly one division (yes, it is unusual requirement). - Each problem used in division 1 should be harder than any problem used in division 2. - If two problems are similar, they should be used in different divisions.
Your goal is count the number of ways to split problem between two divisions and satisfy all the rules. Two ways to split problems are considered to be different if there is at least one problem that belongs to division 1 in one of them and to division 2 in the other.
Note, that the relation of similarity is not transitive. That is, if problem *i* is similar to problem *j* and problem *j* is similar to problem *k*, it doesn't follow that *i* is similar to *k*. | The first line of the input contains two integers *n* and *m* (2<=≤<=*n*<=≤<=100<=000, 0<=≤<=*m*<=≤<=100<=000) — the number of problems prepared for the round and the number of pairs of similar problems, respectively.
Each of the following *m* lines contains a pair of similar problems *u**i* and *v**i* (1<=≤<=*u**i*,<=*v**i*<=≤<=*n*,<=*u**i*<=≠<=*v**i*). It's guaranteed, that no pair of problems meets twice in the input. | Print one integer — the number of ways to split problems in two divisions. | [
"5 2\n1 4\n5 2\n",
"3 3\n1 2\n2 3\n1 3\n",
"3 2\n3 1\n3 2\n"
] | [
"2\n",
"0\n",
"1\n"
] | In the first sample, problems 1 and 2 should be used in division 2, while problems 4 and 5 in division 1. Problem 3 may be used either in division 1 or in division 2.
In the second sample, all pairs of problems are similar and there is no way to split problem between two divisions without breaking any rules.
Third sample reminds you that the similarity relation is not transitive. Problem 3 is similar to both 1 and 2, but 1 is not similar to 2, so they may be used together. | [
{
"input": "5 2\n1 4\n5 2",
"output": "2"
},
{
"input": "3 3\n1 2\n2 3\n1 3",
"output": "0"
},
{
"input": "3 2\n3 1\n3 2",
"output": "1"
},
{
"input": "2 0",
"output": "1"
},
{
"input": "2 1\n1 2",
"output": "1"
},
{
"input": "3 0",
"output": "2"
},
{
"input": "3 1\n1 2",
"output": "1"
},
{
"input": "3 1\n1 3",
"output": "2"
},
{
"input": "100000 0",
"output": "99999"
},
{
"input": "4 2\n1 2\n3 4",
"output": "0"
},
{
"input": "3 1\n2 3",
"output": "1"
},
{
"input": "3 2\n1 2\n1 3",
"output": "1"
},
{
"input": "3 2\n1 2\n2 3",
"output": "0"
},
{
"input": "4 0",
"output": "3"
},
{
"input": "100000 1\n100000 1",
"output": "99999"
},
{
"input": "100000 1\n26711 97965",
"output": "71254"
},
{
"input": "100000 10\n99562 479\n643 99684\n593 99867\n99529 175\n99738 616\n99523 766\n99503 121\n99784 158\n199 99199\n15 99849",
"output": "98433"
},
{
"input": "10 10\n8 3\n2 8\n3 7\n3 9\n9 4\n7 2\n1 8\n1 9\n10 2\n10 1",
"output": "3"
},
{
"input": "55 1\n55 1",
"output": "54"
},
{
"input": "4 2\n1 4\n3 2",
"output": "1"
},
{
"input": "5 1\n1 5",
"output": "4"
},
{
"input": "7 1\n3 5",
"output": "2"
},
{
"input": "7 2\n1 6\n2 7",
"output": "4"
},
{
"input": "5 1\n2 3",
"output": "1"
},
{
"input": "5 2\n3 5\n1 2",
"output": "0"
},
{
"input": "4 2\n3 4\n1 2",
"output": "0"
},
{
"input": "7 2\n1 5\n5 2",
"output": "3"
},
{
"input": "7 2\n1 3\n3 6",
"output": "0"
},
{
"input": "10 11\n1 10\n1 9\n1 8\n1 7\n2 10\n2 9\n2 8\n2 7\n3 10\n3 9\n3 8",
"output": "4"
},
{
"input": "4 2\n1 2\n1 3",
"output": "1"
}
] | 61 | 4,608,000 | 0 | 13,114 |
|
36 | Bowls | [
"geometry",
"implementation"
] | C. Bowls | 2 | 64 | Once Petya was in such a good mood that he decided to help his mum with the washing-up. There were *n* dirty bowls in the sink. From the geometrical point of view each bowl looks like a blunted cone. We can disregard the width of the walls and bottom. Petya puts the clean bowls one on another naturally, i. e. so that their vertical axes coincide (see the picture). You will be given the order in which Petya washes the bowls. Determine the height of the construction, i.e. the distance from the bottom of the lowest bowl to the top of the highest one. | The first input line contains integer *n* (1<=≤<=*n*<=≤<=3000). Each of the following *n* lines contains 3 integers *h*, *r* and *R* (1<=≤<=*h*<=≤<=10000,<=1<=≤<=*r*<=<<=*R*<=≤<=10000). They are the height of a bowl, the radius of its bottom and the radius of its top. The plates are given in the order Petya puts them on the table. | Output the height of the plate pile accurate to at least 10<=-<=6. | [
"2\n40 10 50\n60 20 30\n",
"3\n50 30 80\n35 25 70\n40 10 90\n"
] | [
"70.00000000\n",
"55.00000000\n"
] | none | [
{
"input": "2\n40 10 50\n60 20 30",
"output": "70.00000000"
},
{
"input": "3\n50 30 80\n35 25 70\n40 10 90",
"output": "55.00000000"
},
{
"input": "1\n5 3 10",
"output": "5.00000000"
},
{
"input": "3\n1 1 2\n2 2 3\n3 3 4",
"output": "6.00000000"
},
{
"input": "3\n3 3 4\n2 2 3\n1 1 2",
"output": "3.00000000"
},
{
"input": "2\n3 3 5\n1 4 5",
"output": "3.00000000"
},
{
"input": "2\n4 5 8\n10 6 7",
"output": "11.33333333"
},
{
"input": "3\n4 5 8\n1 1 2\n5 3 4",
"output": "6.00000000"
},
{
"input": "2\n4 5 8\n1 2 7",
"output": "4.00000000"
},
{
"input": "2\n1 1 2\n1 1 2",
"output": "1.00000000"
},
{
"input": "10\n18 3 5\n17 10 20\n1 12 18\n17 14 16\n15 10 19\n7 11 14\n3 11 12\n16 18 19\n13 17 20\n20 18 20",
"output": "82.93333333"
},
{
"input": "10\n6 18 19\n2 6 7\n2 11 16\n10 1 3\n16 1 10\n5 14 15\n12 15 18\n5 15 19\n16 4 16\n14 4 18",
"output": "55.69444444"
},
{
"input": "10\n13 11 15\n8 2 17\n10 10 18\n11 7 10\n10 14 16\n3 13 14\n20 1 20\n14 9 13\n19 7 10\n8 10 20",
"output": "56.75438596"
},
{
"input": "10\n1 4 12\n13 16 18\n11 6 9\n5 14 15\n12 7 18\n9 13 15\n17 2 17\n15 5 14\n2 10 14\n3 16 20",
"output": "39.94545455"
},
{
"input": "10\n20 19 20\n10 15 19\n12 6 9\n6 1 12\n14 17 19\n7 13 19\n6 6 14\n4 2 5\n5 16 18\n17 2 13",
"output": "43.63636364"
},
{
"input": "10\n8 12 19\n15 10 11\n1 5 20\n19 7 10\n7 11 13\n4 13 16\n14 11 12\n13 15 20\n1 19 20\n11 8 10",
"output": "77.73333333"
},
{
"input": "10\n15 5 19\n20 6 16\n2 1 15\n1 13 18\n9 5 13\n2 13 20\n11 15 18\n1 12 13\n4 3 4\n5 14 19",
"output": "42.04285714"
},
{
"input": "10\n3 1 9\n5 2 19\n11 19 20\n2 19 20\n11 15 19\n8 12 14\n19 17 18\n10 5 6\n7 9 10\n19 1 13",
"output": "51.94117647"
},
{
"input": "10\n10 13 18\n2 16 18\n12 18 19\n15 7 8\n12 9 16\n6 12 16\n16 2 14\n19 2 8\n10 12 14\n13 3 11",
"output": "63.00000000"
},
{
"input": "10\n1 4 17\n10 10 12\n11 4 12\n20 19 20\n1 16 20\n16 13 20\n13 2 9\n3 13 16\n8 17 19\n9 4 7",
"output": "55.46153846"
}
] | 92 | 0 | 0 | 13,158 |
802 | Fake News (medium) | [
"constructive algorithms",
"strings"
] | null | null | Thanks to your help, Heidi is confident that no one can fool her. She has now decided to post some fake news on the HC2 Facebook page. However, she wants to be able to communicate to the HC2 committee that the post is fake, using some secret phrase hidden in the post as a subsequence. To make this method foolproof, she wants the phrase to appear *n* times in the post. She is asking you to design a post (string) *s* and a hidden phrase *p* such that *p* appears in *s* as a subsequence exactly *n* times. | The first and only line of input contains a single integer *n* (1<=≤<=*n*<=≤<=1<=000<=000). | The output should contain two nonempty strings *s* and *p* separated by a single space. Each string should be composed of letters (a-z and A-Z: both lowercase and uppercase are allowed) and have length at most 200. The number of occurrences of *p* in *s* as a subsequence should be exactly *n*. If there are many possible solutions, output any of them. It is guaranteed that at least one solution exists. | [
"2\n",
"4\n",
"6\n"
] | [
"hHheidi Hei",
"bbbba ba",
"aaabb ab"
] | An occurrence of *p* as a subsequence in *s* should be thought of as a set of positions in *s* such that the letters at these positions, in order, form *p*. The number of occurences is thus the number of such sets. For example, ab appears 6 times as a subsequence in aaabb, for the following sets of positions: {1, 4}, {1, 5}, {2, 4}, {2, 5}, {3, 4}, {3, 5} (that is, we should choose one of the a's and one of the b's). | [
{
"input": "2",
"output": "aa a"
},
{
"input": "4",
"output": "bbbba ba"
},
{
"input": "6",
"output": "bbabba ba"
},
{
"input": "1",
"output": "a a"
},
{
"input": "3",
"output": "bbba ba"
},
{
"input": "5",
"output": "bbaba ba"
},
{
"input": "999983",
"output": "ssrrqqppoonnmmllkkjjiihhggffeeddccbbabcejnosrqponmlkjihgfedcba srqponmlkjihgfedcba"
},
{
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"output": "ssrrqqppoonnmmllkkjjiihhggffeeddccbbabcejmssrqponmlkjihgfedcba srqponmlkjihgfedcba"
},
{
"input": "7",
"output": "ccbbcba cba"
},
{
"input": "8",
"output": "ccbbccba cba"
},
{
"input": "9",
"output": "ccbbbcba cba"
},
{
"input": "10",
"output": "ccbbbccba cba"
},
{
"input": "11",
"output": "ccbbacba cba"
},
{
"input": "12",
"output": "ccbbaccba cba"
},
{
"input": "13",
"output": "ccbbabcba cba"
},
{
"input": "14",
"output": "ccbbabccba cba"
},
{
"input": "15",
"output": "ddccbbdcba dcba"
},
{
"input": "16",
"output": "ddccbbddcba dcba"
},
{
"input": "17",
"output": "ddccbbcdcba dcba"
},
{
"input": "18",
"output": "ddccbbcddcba dcba"
},
{
"input": "19",
"output": "ddccbbbdcba dcba"
},
{
"input": "20",
"output": "ddccbbbddcba dcba"
},
{
"input": "21",
"output": "ddccbbbcdcba dcba"
},
{
"input": "22",
"output": "ddccbbbcddcba dcba"
},
{
"input": "23",
"output": "ddccbbadcba dcba"
},
{
"input": "24",
"output": "ddccbbaddcba dcba"
},
{
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"output": "ddccbbacdcba dcba"
},
{
"input": "26",
"output": "ddccbbacddcba dcba"
},
{
"input": "27",
"output": "ddccbbabdcba dcba"
},
{
"input": "28",
"output": "ddccbbabddcba dcba"
},
{
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"output": "ddccbbabcdcba dcba"
},
{
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},
{
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"input": "604309",
"output": "ssrrqqppoonnmmllkkjjiihhggffeeddccbbcfghloqrsrqponmlkjihgfedcba srqponmlkjihgfedcba"
},
{
"input": "176389",
"output": "qqppoonnmmllkkjjiihhggffeeddccbbbdeiopqponmlkjihgfedcba qponmlkjihgfedcba"
},
{
"input": "58997",
"output": "oonnmmllkkjjiihhggffeeddccbbabefijkmnonmlkjihgfedcba onmlkjihgfedcba"
},
{
"input": "652591",
"output": "ssrrqqppoonnmmllkkjjiihhggffeeddccbbcdefgiknosrqponmlkjihgfedcba srqponmlkjihgfedcba"
},
{
"input": "995699",
"output": "ssrrqqppoonnmmllkkjjiihhggffeeddccbbabcfgkmnoqsrqponmlkjihgfedcba srqponmlkjihgfedcba"
},
{
"input": "635909",
"output": "ssrrqqppoonnmmllkkjjiihhggffeeddccbbcdfgiqrsrqponmlkjihgfedcba srqponmlkjihgfedcba"
},
{
"input": "193841",
"output": "qqppoonnmmllkkjjiihhggffeeddccbbbcdegilmpqponmlkjihgfedcba qponmlkjihgfedcba"
},
{
"input": "467503",
"output": "rrqqppoonnmmllkkjjiihhggffeeddccbbabeimnrqponmlkjihgfedcba rqponmlkjihgfedcba"
}
] | 31 | 0 | -1 | 13,184 |
|
911 | Inversion Counting | [
"brute force",
"math"
] | null | null | A permutation of size *n* is an array of size *n* such that each integer from 1 to *n* occurs exactly once in this array. An inversion in a permutation *p* is a pair of indices (*i*,<=*j*) such that *i*<=><=*j* and *a**i*<=<<=*a**j*. For example, a permutation [4,<=1,<=3,<=2] contains 4 inversions: (2,<=1), (3,<=1), (4,<=1), (4,<=3).
You are given a permutation *a* of size *n* and *m* queries to it. Each query is represented by two indices *l* and *r* denoting that you have to reverse the segment [*l*,<=*r*] of the permutation. For example, if *a*<==<=[1,<=2,<=3,<=4] and a query *l*<==<=2, *r*<==<=4 is applied, then the resulting permutation is [1,<=4,<=3,<=2].
After each query you have to determine whether the number of inversions is odd or even. | The first line contains one integer *n* (1<=≤<=*n*<=≤<=1500) — the size of the permutation.
The second line contains *n* integers *a*1, *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=*n*) — the elements of the permutation. These integers are pairwise distinct.
The third line contains one integer *m* (1<=≤<=*m*<=≤<=2·105) — the number of queries to process.
Then *m* lines follow, *i*-th line containing two integers *l**i*, *r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*) denoting that *i*-th query is to reverse a segment [*l**i*,<=*r**i*] of the permutation. All queries are performed one after another. | Print *m* lines. *i*-th of them must be equal to odd if the number of inversions in the permutation after *i*-th query is odd, and even otherwise. | [
"3\n1 2 3\n2\n1 2\n2 3\n",
"4\n1 2 4 3\n4\n1 1\n1 4\n1 4\n2 3\n"
] | [
"odd\neven\n",
"odd\nodd\nodd\neven\n"
] | The first example:
1. after the first query *a* = [2, 1, 3], inversion: (2, 1); 1. after the second query *a* = [2, 3, 1], inversions: (3, 1), (3, 2).
The second example:
1. *a* = [1, 2, 4, 3], inversion: (4, 3); 1. *a* = [3, 4, 2, 1], inversions: (3, 1), (4, 1), (3, 2), (4, 2), (4, 3); 1. *a* = [1, 2, 4, 3], inversion: (4, 3); 1. *a* = [1, 4, 2, 3], inversions: (3, 2), (4, 2). | [
{
"input": "3\n1 2 3\n2\n1 2\n2 3",
"output": "odd\neven"
},
{
"input": "4\n1 2 4 3\n4\n1 1\n1 4\n1 4\n2 3",
"output": "odd\nodd\nodd\neven"
},
{
"input": "7\n2 6 1 7 4 5 3\n5\n4 5\n7 7\n5 6\n4 5\n4 5",
"output": "odd\nodd\neven\nodd\neven"
},
{
"input": "3\n2 1 3\n3\n2 3\n1 1\n1 3",
"output": "even\neven\nodd"
},
{
"input": "1\n1\n10\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1",
"output": "even\neven\neven\neven\neven\neven\neven\neven\neven\neven"
}
] | 451 | 13,312,000 | 3 | 13,194 |
|
156 | Cipher | [
"combinatorics",
"dp"
] | null | null | Sherlock Holmes found a mysterious correspondence of two VIPs and made up his mind to read it. But there is a problem! The correspondence turned out to be encrypted. The detective tried really hard to decipher the correspondence, but he couldn't understand anything.
At last, after some thought, he thought of something. Let's say there is a word *s*, consisting of |*s*| lowercase Latin letters. Then for one operation you can choose a certain position *p* (1<=≤<=*p*<=<<=|*s*|) and perform one of the following actions:
- either replace letter *s**p* with the one that alphabetically follows it and replace letter *s**p*<=+<=1 with the one that alphabetically precedes it; - or replace letter *s**p* with the one that alphabetically precedes it and replace letter *s**p*<=+<=1 with the one that alphabetically follows it.
Let us note that letter "z" doesn't have a defined following letter and letter "a" doesn't have a defined preceding letter. That's why the corresponding changes are not acceptable. If the operation requires performing at least one unacceptable change, then such operation cannot be performed.
Two words coincide in their meaning iff one of them can be transformed into the other one as a result of zero or more operations.
Sherlock Holmes needs to learn to quickly determine the following for each word: how many words can exist that coincide in their meaning with the given word, but differs from the given word in at least one character? Count this number for him modulo 1000000007 (109<=+<=7). | The input data contains several tests. The first line contains the only integer *t* (1<=≤<=*t*<=≤<=104) — the number of tests.
Next *t* lines contain the words, one per line. Each word consists of lowercase Latin letters and has length from 1 to 100, inclusive. Lengths of words can differ. | For each word you should print the number of different other words that coincide with it in their meaning — not from the words listed in the input data, but from all possible words. As the sought number can be very large, print its value modulo 1000000007 (109<=+<=7). | [
"1\nab\n",
"1\naaaaaaaaaaa\n",
"2\nya\nklmbfxzb\n"
] | [
"1\n",
"0\n",
"24\n320092793\n"
] | Some explanations about the operation:
- Note that for each letter, we can clearly define the letter that follows it. Letter "b" alphabetically follows letter "a", letter "c" follows letter "b", ..., "z" follows letter "y". - Preceding letters are defined in the similar manner: letter "y" precedes letter "z", ..., "a" precedes letter "b". - Note that the operation never changes a word's length.
In the first sample you can obtain the only other word "ba". In the second sample you cannot obtain any other word, so the correct answer is 0.
Consider the third sample. One operation can transform word "klmbfxzb" into word "klmcexzb": we should choose *p* = 4, and replace the fourth letter with the following one ("b" → "c"), and the fifth one — with the preceding one ("f" → "e"). Also, we can obtain many other words from this one. An operation can transform word "ya" only into one other word "xb".
Word "ya" coincides in its meaning with words "xb", "wc", "vd", ..., "ay" (overall there are 24 other words). The word "klmbfxzb has many more variants — there are 3320092814 other words that coincide with in the meaning. So the answer for the first word equals 24 and for the second one equals 320092793 — the number 3320092814 modulo 10<sup class="upper-index">9</sup> + 7 | [
{
"input": "1\nab",
"output": "1"
},
{
"input": "1\naaaaaaaaaaa",
"output": "0"
},
{
"input": "2\nya\nklmbfxzb",
"output": "24\n320092793"
},
{
"input": "1\na",
"output": "0"
},
{
"input": "1\nz",
"output": "0"
},
{
"input": "1\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"output": "0"
},
{
"input": "1\nmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmn",
"output": "39086755"
},
{
"input": "15\nejkf\nkc\nu\nznmjnznzn\nbjkcg\nwou\nywy\nqoojqlr\nnbkip\nsgmgjg\ndjjdd\nh\nkgbkri\nt\npvzbvkij",
"output": "4454\n12\n0\n667098198\n35884\n209\n20\n142184034\n186649\n4212829\n31439\n0\n3167654\n0\n474922754"
},
{
"input": "15\nieqqe\nwwbnobrb\ngyftfg\nclrn\nzwtviipwww\nmsmsiih\nofqsusmsmm\nyjomiiq\naedoeun\nz\nmwwmimiwiu\ngtdsifgg\nvmmmren\nzlgzousxzp\ngcpodkxebk",
"output": "195974\n543885418\n5715485\n10619\n87838649\n154292634\n869212338\n155736014\n55669004\n0\n792902040\n590044032\n155736014\n991368939\n271743066"
},
{
"input": "17\nwfvfmnmr\nkyururk\nnei\nmeb\nwldtalawww\njeobzb\nuuww\nwfkgzxmr\nrvvpxrihha\nqz\ngpodf\niatnevlia\njjnaunradf\nwoi\ny\nmewdykdldp\nnckg",
"output": "662991818\n51681734\n350\n170\n598684361\n3582684\n968\n541474246\n55368153\n9\n148439\n157054204\n91519085\n464\n0\n838428119\n5759"
},
{
"input": "17\nku\njf\nygbkcbf\ngmp\nnuaxjssqv\nawxxcxw\nyccccvc\na\nu\nnod\nmfgtj\nekkjbkzr\njtisatba\nxtkxlk\nt\nxkxzuizs\nnvvvqarn",
"output": "20\n14\n25664534\n486\n516112667\n64053170\n44165015\n0\n0\n450\n222299\n145570718\n897496632\n3582684\n0\n190441484\n326269025"
},
{
"input": "19\nqhovyphr\nttymgy\nqbed\nidxitl\nusbrx\nqevvydqdb\nltyjljj\ncgv\nsruvudcu\naqjbqjybyq\nrhtwwtthhh\nh\nksktyyst\npmwmnzswlw\nm\nuwaup\nxhvk\nj\nvii",
"output": "434174305\n2030279\n2924\n6460404\n177169\n583243193\n154292634\n434\n434174305\n191795714\n792902040\n0\n573191111\n676498805\n0\n195974\n9239\n0\n506"
},
{
"input": "10\njrojjyqqjtrfjf\nvuwzvmwjyfvifdfddymwfuzmvvummwdfzjzdvzuvfvjiuvyzymviyyumvziyimfzfiji\nwxzwojjzqzyqlojjbrjlbqrrwqw\nqfwppnuvbgegbqgbmeqpbguwmmqhunnquepepeewubbmnenvmwhnvhunnmsqmmgfepevupewvenmwpmgspnebv\nrxqzorkizznsiirciokscrrjqqqzkfijrrkkfrqjjifczcjcnqoisorszkjxcxvqzcfczqfcrvfrsckvvfjxnxzqjivqv\nnvimavvhfskwkhgvaowsficdmv\nqvrdgohdmgawrqo\npulanukntfhrthkxkprprhrhcouxxnkhoroptcxkfktotkokonoxptcocnfartlucnlncalnknhlpachofclannctpklackcc\ntqezktgzhipiaootfpqpzjgtqitagthef\nqaeigcacoqoc",
"output": "520219051\n945235283\n691128313\n324077859\n417775814\n827035318\n275780270\n145635612\n155578699\n486064325"
},
{
"input": "10\nnnclytzybytthncihlnnbclzcbhinhyzbhnbiyccltnnchylynhznycniiztzcthiyyhccybc\ngbcccdnjbgntyzayntwdf\ndzkxapreirktspflaudtlexeffifxxzxrjaxqfkcncxf\nnilfxfsyliingzbgsxbzxxmqqxnngsfqqqbqinglmbxgysbi\nsjquzchhssjrrzbuc\nhdhvdnjvhreiiekeinvdddneejkrdkjvikj\nanyamaosolahmhnmsmmmmhhofsaalfmomoshy\nnqvzznlicebqsviwivvhhiiciblbelvlelhisclecb\nlbtihlhulugddgtfwjiftfltijwitcgmgvjfcfcdwbliijqhidghdwibpgjqdumdijmhlbdfvcpcqqptcc\nkfjcmfzxhhkhfikihymhmhxuzeykfkmezcmieyxxshjckfxsx",
"output": "860385290\n566220124\n563237657\n25482967\n365565922\n211740598\n627945017\n550126162\n997587067\n505019519"
}
] | 964 | 8,601,600 | 3 | 13,250 |
|
316 | EKG | [
"dfs and similar",
"dp"
] | null | null | In the rush of modern life, people often forget how beautiful the world is. The time to enjoy those around them is so little that some even stand in queues to several rooms at the same time in the clinic, running from one queue to another.
(Cultural note: standing in huge and disorganized queues for hours is a native tradition in Russia, dating back to the Soviet period. Queues can resemble crowds rather than lines. Not to get lost in such a queue, a person should follow a strict survival technique: you approach the queue and ask who the last person is, somebody answers and you join the crowd. Now you're the last person in the queue till somebody else shows up. You keep an eye on the one who was last before you as he is your only chance to get to your destination) I'm sure many people have had the problem when a stranger asks who the last person in the queue is and even dares to hint that he will be the last in the queue and then bolts away to some unknown destination. These are the representatives of the modern world, in which the ratio of lack of time is so great that they do not even watch foreign top-rated TV series. Such people often create problems in queues, because the newcomer does not see the last person in the queue and takes a place after the "virtual" link in this chain, wondering where this legendary figure has left.
The Smart Beaver has been ill and he's made an appointment with a therapist. The doctor told the Beaver the sad news in a nutshell: it is necessary to do an electrocardiogram. The next day the Smart Beaver got up early, put on the famous TV series on download (three hours till the download's complete), clenched his teeth and bravely went to join a queue to the electrocardiogram room, which is notorious for the biggest queues at the clinic.
Having stood for about three hours in the queue, the Smart Beaver realized that many beavers had not seen who was supposed to stand in the queue before them and there was a huge mess. He came up to each beaver in the ECG room queue and asked who should be in front of him in the queue. If the beaver did not know his correct position in the queue, then it might be his turn to go get an ECG, or maybe he should wait for a long, long time...
As you've guessed, the Smart Beaver was in a hurry home, so he gave you all the necessary information for you to help him to determine what his number in the queue can be. | The first line contains two integers *n* (1<=≤<=*n*<=≤<=103) and *x* (1<=≤<=*x*<=≤<=*n*) — the number of beavers that stand in the queue and the Smart Beaver's number, correspondingly. All willing to get to the doctor are numbered from 1 to *n*.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=*n*) — the number of the beaver followed by the *i*-th beaver. If *a**i*<==<=0, then the *i*-th beaver doesn't know who is should be in front of him. It is guaranteed that values *a**i* are correct. That is there is no cycles in the dependencies. And any beaver is followed by at most one beaver in the queue.
The input limits for scoring 30 points are (subproblem B1):
- It is guaranteed that the number of zero elements *a**i* doesn't exceed 20.
The input limits for scoring 100 points are (subproblems B1+B2):
- The number of zero elements *a**i* is arbitrary. | Print all possible positions of the Smart Beaver in the line in the increasing order. | [
"6 1\n2 0 4 0 6 0\n",
"6 2\n2 3 0 5 6 0\n",
"4 1\n0 0 0 0\n",
"6 2\n0 0 1 0 4 5\n"
] | [
"2\n4\n6\n",
"2\n5\n",
"1\n2\n3\n4\n",
"1\n3\n4\n6\n"
] | [
{
"input": "6 1\n2 0 4 0 6 0",
"output": "2\n4\n6"
},
{
"input": "6 2\n2 3 0 5 6 0",
"output": "2\n5"
},
{
"input": "4 1\n0 0 0 0",
"output": "1\n2\n3\n4"
},
{
"input": "6 2\n0 0 1 0 4 5",
"output": "1\n3\n4\n6"
},
{
"input": "10 7\n10 8 6 5 0 0 0 4 3 9",
"output": "1\n5\n6\n10"
},
{
"input": "10 1\n8 7 0 2 0 10 0 0 3 5",
"output": "2\n4\n5\n7\n8\n10"
},
{
"input": "10 4\n0 1 4 2 7 0 10 0 5 8",
"output": "3\n4\n8\n9"
},
{
"input": "10 2\n0 7 0 10 8 0 4 2 3 0",
"output": "4\n5\n6\n7\n8"
},
{
"input": "10 2\n10 0 9 0 0 4 2 6 8 0",
"output": "1\n2\n3\n4\n6\n7\n8\n9"
},
{
"input": "10 7\n7 9 2 10 0 0 0 3 5 1",
"output": "1\n2\n6\n7"
},
{
"input": "20 20\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"output": "1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n19\n20"
}
] | 140 | 2,764,800 | 3 | 13,256 |
||
291 | Parallel Programming | [
"*special",
"greedy"
] | null | null | Polycarpus has a computer with *n* processors. Also, his computer has *n* memory cells. We'll consider the processors numbered by integers from 1 to *n* and that the memory cells are consecutively numbered by integers from 1 to *n*.
Polycarpus needs to come up with a parallel program model. For each memory cell number *i* this program must record the value *n*<=-<=*i* to this cell. In other words, for each cell you've got to find the distance to cell *n*.
Let's denote the value that is written in the *i*-th cell as *a**i*. Initially, *a**i*<==<=1 (1<=≤<=*i*<=<<=*n*) and *a**n*<==<=0. We will consider that only processor *i* can write values in the memory cell number *i*. All processors can read an information from some cell (several processors can read an information from some cell simultaneously).
The parallel program is executed in several steps. During each step we execute the parallel version of the increment operation. Executing the parallel version of the increment operation goes as follows:
1. Each processor independently of the other ones chooses some memory cell. Let's say that processor *i* has chosen a cell with number *c**i* (1<=≤<=*c**i*<=≤<=*n*). 1. All processors simultaneously execute operation *a**i*<==<=*a**i*<=+<=*a**c**i*.
Help Polycarpus come up with the parallel program model that is executed in exactly *k* steps. Calculate the operations that need to be executed. Note that after *k* steps for all *i*'s value *a**i* must be equal *n*<=-<=*i*. | The first line contains two space-separated integers *n* and *k* (1<=≤<=*n*<=≤<=104,<=1<=≤<=*k*<=≤<=20).
It is guaranteed that at the given *n* and *k* the required sequence of operations exists. | Print exactly *n*·*k* integers in *k* lines. In the first line print numbers *c*1,<=*c*2,<=...,<=*c**n* (1<=≤<=*c**i*<=≤<=*n*) for the first increment operation. In the second line print the numbers for the second increment operation. In the *k*-th line print the numbers for the *k*-th increment operation.
As a result of the printed operations for any *i* value *a**i* must equal *n*<=-<=*i*. | [
"1 1\n",
"3 2\n"
] | [
"1\n",
"2 3 3\n3 3 3\n"
] | none | [
{
"input": "1 1",
"output": "1"
},
{
"input": "3 2",
"output": "2 3 3\n3 3 3"
},
{
"input": "4 2",
"output": "2 3 4 4\n3 4 4 4"
},
{
"input": "2 1",
"output": "2 2"
},
{
"input": "2 20",
"output": "2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2\n2 2"
},
{
"input": "1 20",
"output": "1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1"
},
{
"input": "10000 20",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "10 4",
"output": "2 3 4 5 6 7 8 9 10 10\n3 4 5 6 7 8 9 10 10 10\n5 6 7 8 9 10 10 10 10 10\n9 10 10 10 10 10 10 10 10 10"
},
{
"input": "10 5",
"output": "2 3 4 5 6 7 8 9 10 10\n3 4 5 6 7 8 9 10 10 10\n5 6 7 8 9 10 10 10 10 10\n9 10 10 10 10 10 10 10 10 10\n10 10 10 10 10 10 10 10 10 10"
},
{
"input": "10 6",
"output": "2 3 4 5 6 7 8 9 10 10\n3 4 5 6 7 8 9 10 10 10\n5 6 7 8 9 10 10 10 10 10\n9 10 10 10 10 10 10 10 10 10\n10 10 10 10 10 10 10 10 10 10\n10 10 10 10 10 10 10 10 10 10"
},
{
"input": "128 7",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 128\n3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 ..."
},
{
"input": "127 7",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 127\n3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4..."
},
{
"input": "129 8",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 129\n3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38..."
},
{
"input": "130 8",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 130\n3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3..."
},
{
"input": "131 8",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 131\n3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 ..."
},
{
"input": "1024 10",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "1024 11",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "1023 10",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "10000 14",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "8192 13",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "8190 13",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "8192 14",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "8123 13",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "5000 13",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "2000 11",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "2198 14",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "2512 12",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
}
] | 92 | 0 | 0 | 13,263 |
|
396 | On Sum of Fractions | [
"math",
"number theory"
] | null | null | Let's assume that
- *v*(*n*) is the largest prime number, that does not exceed *n*;- *u*(*n*) is the smallest prime number strictly greater than *n*.
Find . | The first line contains integer *t* (1<=≤<=*t*<=≤<=500) — the number of testscases.
Each of the following *t* lines of the input contains integer *n* (2<=≤<=*n*<=≤<=109). | Print *t* lines: the *i*-th of them must contain the answer to the *i*-th test as an irreducible fraction "*p*/*q*", where *p*,<=*q* are integers, *q*<=><=0. | [
"2\n2\n3\n"
] | [
"1/6\n7/30\n"
] | none | [
{
"input": "2\n2\n3",
"output": "1/6\n7/30"
},
{
"input": "1\n1000000000",
"output": "999999941999999673/1999999887999999118"
},
{
"input": "5\n3\n6\n9\n10\n5",
"output": "7/30\n5/14\n61/154\n9/22\n23/70"
},
{
"input": "5\n5\n8\n18\n17\n17",
"output": "23/70\n59/154\n17/38\n287/646\n287/646"
},
{
"input": "5\n7\n40\n37\n25\n4",
"output": "57/154\n39/82\n1437/3034\n615/1334\n3/10"
},
{
"input": "5\n72\n72\n30\n75\n11",
"output": "71/146\n71/146\n29/62\n5615/11534\n119/286"
},
{
"input": "5\n79\n149\n136\n194\n124",
"output": "6393/13114\n22199/44998\n135/274\n37631/76042\n14121/28702"
},
{
"input": "6\n885\n419\n821\n635\n63\n480",
"output": "781453/1566442\n175559/352798\n674039/1351366\n403199/808942\n3959/8174\n232303/466546"
},
{
"input": "1\n649580447",
"output": "421954771415489597/843909545429301074"
}
] | 46 | 307,200 | 0 | 13,273 |
|
290 | Mysterious strings | [
"*special",
"implementation"
] | null | null | The input contains a single integer *a* (1<=≤<=*a*<=≤<=40).
Output a single string. | The input contains a single integer *a* (1<=≤<=*a*<=≤<=40). | Output a single string. | [
"2\n",
"8\n",
"29\n"
] | [
"Adams\n",
"Van Buren\n",
"Harding\n"
] | none | [
{
"input": "2",
"output": "Adams"
},
{
"input": "8",
"output": "Van Buren"
},
{
"input": "29",
"output": "Harding"
},
{
"input": "1",
"output": "Washington"
},
{
"input": "3",
"output": "Jefferson"
},
{
"input": "4",
"output": "Madison"
},
{
"input": "5",
"output": "Monroe"
},
{
"input": "6",
"output": "Adams"
},
{
"input": "7",
"output": "Jackson"
},
{
"input": "9",
"output": "Harrison"
},
{
"input": "10",
"output": "Tyler"
},
{
"input": "11",
"output": "Polk"
},
{
"input": "12",
"output": "Taylor"
},
{
"input": "13",
"output": "Fillmore"
},
{
"input": "14",
"output": "Pierce"
},
{
"input": "15",
"output": "Buchanan"
},
{
"input": "16",
"output": "Lincoln"
},
{
"input": "17",
"output": "Johnson"
},
{
"input": "18",
"output": "Grant"
},
{
"input": "19",
"output": "Hayes"
},
{
"input": "20",
"output": "Garfield"
},
{
"input": "21",
"output": "Arthur"
},
{
"input": "22",
"output": "Cleveland"
},
{
"input": "23",
"output": "Harrison"
},
{
"input": "24",
"output": "Cleveland"
},
{
"input": "25",
"output": "McKinley"
},
{
"input": "26",
"output": "Roosevelt"
},
{
"input": "27",
"output": "Taft"
},
{
"input": "28",
"output": "Wilson"
},
{
"input": "30",
"output": "Coolidge"
},
{
"input": "31",
"output": "Hoover"
},
{
"input": "32",
"output": "Roosevelt"
},
{
"input": "33",
"output": "Truman"
},
{
"input": "34",
"output": "Eisenhower"
},
{
"input": "35",
"output": "Kennedy"
},
{
"input": "36",
"output": "Johnson"
},
{
"input": "37",
"output": "Nixon"
},
{
"input": "38",
"output": "Ford"
},
{
"input": "39",
"output": "Carter"
},
{
"input": "40",
"output": "Reagan"
}
] | 62 | 0 | 0 | 13,329 |
|
567 | One-Dimensional Battle Ships | [
"binary search",
"data structures",
"greedy",
"sortings"
] | null | null | Alice and Bob love playing one-dimensional battle ships. They play on the field in the form of a line consisting of *n* square cells (that is, on a 1<=×<=*n* table).
At the beginning of the game Alice puts *k* ships on the field without telling their positions to Bob. Each ship looks as a 1<=×<=*a* rectangle (that is, it occupies a sequence of *a* consecutive squares of the field). The ships cannot intersect and even touch each other.
After that Bob makes a sequence of "shots". He names cells of the field and Alice either says that the cell is empty ("miss"), or that the cell belongs to some ship ("hit").
But here's the problem! Alice like to cheat. May be that is why she responds to each Bob's move with a "miss".
Help Bob catch Alice cheating — find Bob's first move, such that after it you can be sure that Alice cheated. | The first line of the input contains three integers: *n*, *k* and *a* (1<=≤<=*n*,<=*k*,<=*a*<=≤<=2·105) — the size of the field, the number of the ships and the size of each ship. It is guaranteed that the *n*, *k* and *a* are such that you can put *k* ships of size *a* on the field, so that no two ships intersect or touch each other.
The second line contains integer *m* (1<=≤<=*m*<=≤<=*n*) — the number of Bob's moves.
The third line contains *m* distinct integers *x*1,<=*x*2,<=...,<=*x**m*, where *x**i* is the number of the cell where Bob made the *i*-th shot. The cells are numbered from left to right from 1 to *n*. | Print a single integer — the number of such Bob's first move, after which you can be sure that Alice lied. Bob's moves are numbered from 1 to *m* in the order the were made. If the sought move doesn't exist, then print "-1". | [
"11 3 3\n5\n4 8 6 1 11\n",
"5 1 3\n2\n1 5\n",
"5 1 3\n1\n3\n"
] | [
"3\n",
"-1\n",
"1\n"
] | none | [
{
"input": "11 3 3\n5\n4 8 6 1 11",
"output": "3"
},
{
"input": "5 1 3\n2\n1 5",
"output": "-1"
},
{
"input": "5 1 3\n1\n3",
"output": "1"
},
{
"input": "1 1 1\n1\n1",
"output": "1"
},
{
"input": "5000 1660 2\n20\n1 100 18 102 300 81 19 25 44 88 1337 4999 1054 1203 91 16 164 914 1419 1487",
"output": "18"
},
{
"input": "5000 1000 2\n3\n1000 2000 3000",
"output": "-1"
},
{
"input": "10 2 4\n2\n5 6",
"output": "-1"
},
{
"input": "10 2 4\n3\n5 6 1",
"output": "3"
},
{
"input": "4 2 1\n2\n1 2",
"output": "2"
},
{
"input": "4 2 1\n2\n1 3",
"output": "-1"
},
{
"input": "50 7 3\n20\n24 18 34 32 44 2 5 40 17 48 31 45 8 6 15 27 26 1 20 10",
"output": "13"
},
{
"input": "50 7 3\n50\n17 47 1 12 21 25 6 5 49 27 34 8 16 38 11 44 48 9 2 20 3 22 33 23 36 41 15 35 31 30 50 7 45 42 37 29 14 26 24 46 19 4 10 28 18 43 32 39 40 13",
"output": "19"
},
{
"input": "50 1 1\n50\n1 13 21 37 30 48 23 19 6 49 36 14 9 24 44 10 41 28 20 2 15 11 45 3 25 33 50 38 35 47 31 4 12 46 32 8 42 26 5 7 27 16 29 43 39 22 17 34 40 18",
"output": "50"
},
{
"input": "200000 100000 1\n1\n31618",
"output": "-1"
},
{
"input": "200000 1 200000\n1\n1",
"output": "1"
},
{
"input": "200000 1 200000\n1\n200000",
"output": "1"
},
{
"input": "200000 1 199999\n2\n1 200000",
"output": "2"
},
{
"input": "200000 1 199999\n2\n200000 1",
"output": "2"
},
{
"input": "200000 1 199999\n2\n2 200000",
"output": "1"
}
] | 124 | 0 | 0 | 13,336 |
|
883 | Photo Processing | [
"binary search",
"dp"
] | null | null | Evlampiy has found one more cool application to process photos. However the application has certain limitations.
Each photo *i* has a contrast *v**i*. In order for the processing to be truly of high quality, the application must receive at least *k* photos with contrasts which differ as little as possible.
Evlampiy already knows the contrast *v**i* for each of his *n* photos. Now he wants to split the photos into groups, so that each group contains at least *k* photos. As a result, each photo must belong to exactly one group.
He considers a processing time of the *j*-th group to be the difference between the maximum and minimum values of *v**i* in the group. Because of multithreading the processing time of a division into groups is the maximum processing time among all groups.
Split *n* photos into groups in a such way that the processing time of the division is the minimum possible, i.e. that the the maximum processing time over all groups as least as possible. | The first line contains two integers *n* and *k* (1<=≤<=*k*<=≤<=*n*<=≤<=3·105) — number of photos and minimum size of a group.
The second line contains *n* integers *v*1,<=*v*2,<=...,<=*v**n* (1<=≤<=*v**i*<=≤<=109), where *v**i* is the contrast of the *i*-th photo. | Print the minimal processing time of the division into groups. | [
"5 2\n50 110 130 40 120\n",
"4 1\n2 3 4 1\n"
] | [
"20\n",
"0\n"
] | In the first example the photos should be split into 2 groups: [40, 50] and [110, 120, 130]. The processing time of the first group is 10, and the processing time of the second group is 20. Maximum among 10 and 20 is 20. It is impossible to split the photos into groups in a such way that the processing time of division is less than 20.
In the second example the photos should be split into four groups, each containing one photo. So the minimal possible processing time of a division is 0. | [
{
"input": "5 2\n50 110 130 40 120",
"output": "20"
},
{
"input": "4 1\n2 3 4 1",
"output": "0"
},
{
"input": "1 1\n4",
"output": "0"
},
{
"input": "2 2\n7 5",
"output": "2"
},
{
"input": "3 2\n34 3 75",
"output": "72"
},
{
"input": "5 2\n932 328 886 96 589",
"output": "343"
},
{
"input": "10 4\n810 8527 9736 3143 2341 6029 7474 707 2513 2023",
"output": "3707"
},
{
"input": "20 11\n924129 939902 178964 918687 720767 695035 577430 407131 213304 810868 596349 266075 123602 376312 36680 18426 716200 121546 61834 851586",
"output": "921476"
},
{
"input": "100 28\n1 2 3 5 1 1 1 4 1 5 2 4 3 2 5 4 1 1 4 1 4 5 4 1 4 5 1 3 5 1 1 1 4 2 5 2 3 5 2 2 3 2 4 5 5 5 5 1 2 4 1 3 1 1 1 4 3 1 5 2 5 1 3 3 2 4 5 1 1 3 4 1 1 3 3 1 2 4 3 3 4 4 3 1 2 1 5 1 4 4 2 3 1 3 3 4 2 4 1 1",
"output": "1"
},
{
"input": "101 9\n3 2 2 1 4 1 3 2 3 4 3 2 3 1 4 4 1 1 4 1 3 3 4 1 2 1 1 3 1 2 2 4 3 1 4 3 1 1 4 4 1 2 1 1 4 2 3 4 1 2 1 4 4 1 4 3 1 4 2 1 2 1 4 3 4 3 4 2 2 4 3 2 1 3 4 3 2 2 4 3 3 2 4 1 3 2 2 4 1 3 4 2 1 3 3 2 2 1 1 3 1",
"output": "0"
},
{
"input": "2 2\n1 1000000000",
"output": "999999999"
},
{
"input": "2 1\n1 1000000000",
"output": "0"
},
{
"input": "11 3\n412 3306 3390 2290 1534 316 1080 2860 253 230 3166",
"output": "1122"
},
{
"input": "10 3\n2414 294 184 666 2706 1999 2201 1270 904 653",
"output": "707"
},
{
"input": "24 4\n33 27 12 65 19 6 46 33 57 2 21 50 73 13 59 69 51 45 39 1 6 64 39 27",
"output": "9"
}
] | 3,000 | 22,118,400 | 0 | 13,405 |
|
0 | none | [
"none"
] | null | null | There are *n* animals in the queue to Dr. Dolittle. When an animal comes into the office, the doctor examines him, gives prescriptions, appoints tests and may appoint extra examination. Doc knows all the forest animals perfectly well and therefore knows exactly that the animal number *i* in the queue will have to visit his office exactly *a**i* times. We will assume that an examination takes much more time than making tests and other extra procedures, and therefore we will assume that once an animal leaves the room, it immediately gets to the end of the queue to the doctor. Of course, if the animal has visited the doctor as many times as necessary, then it doesn't have to stand at the end of the queue and it immediately goes home.
Doctor plans to go home after receiving *k* animals, and therefore what the queue will look like at that moment is important for him. Since the doctor works long hours and she can't get distracted like that after all, she asked you to figure it out. | The first line of input data contains two space-separated integers *n* and *k* (1<=≤<=*n*<=≤<=105, 0<=≤<=*k*<=≤<=1014). In the second line are given space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109).
Please do not use the %lld specificator to read or write 64-bit numbers in C++. It is recommended to use cin, cout streams (you can also use the %I64d specificator). | If the doctor will overall carry out less than *k* examinations, print a single number "-1" (without quotes). Otherwise, print the sequence of numbers — number of animals in the order in which they stand in the queue.
Note that this sequence may be empty. This case is present in pretests. You can just print nothing or print one "End of line"-character. Both will be accepted. | [
"3 3\n1 2 1\n",
"4 10\n3 3 2 1\n",
"7 10\n1 3 3 1 2 3 1\n"
] | [
"2 ",
"-1\n",
"6 2 3 "
] | In the first sample test:
- Before examination: {1, 2, 3} - After the first examination: {2, 3} - After the second examination: {3, 2} - After the third examination: {2}
In the second sample test:
- Before examination: {1, 2, 3, 4, 5, 6, 7} - After the first examination: {2, 3, 4, 5, 6, 7} - After the second examination: {3, 4, 5, 6, 7, 2} - After the third examination: {4, 5, 6, 7, 2, 3} - After the fourth examination: {5, 6, 7, 2, 3} - After the fifth examination: {6, 7, 2, 3, 5} - After the sixth examination: {7, 2, 3, 5, 6} - After the seventh examination: {2, 3, 5, 6} - After the eighth examination: {3, 5, 6, 2} - After the ninth examination: {5, 6, 2, 3} - After the tenth examination: {6, 2, 3} | [
{
"input": "3 3\n1 2 1",
"output": "2 "
},
{
"input": "4 10\n3 3 2 1",
"output": "-1"
},
{
"input": "7 10\n1 3 3 1 2 3 1",
"output": "6 2 3 "
},
{
"input": "1 0\n1",
"output": "1 "
},
{
"input": "6 101\n9 78 54 62 2 91",
"output": "4 6 2 3 "
},
{
"input": "9 100\n11 11 11 11 11 11 11 11 11",
"output": "-1"
},
{
"input": "10 77\n7 45 10 10 9 8 1 2 3 1",
"output": "2 "
},
{
"input": "5 12\n1 3 4 1 5",
"output": "5 "
},
{
"input": "5 23\n7 1 4 7 9",
"output": "1 4 5 "
},
{
"input": "5 41\n19 19 19 15 20",
"output": "2 3 4 5 1 "
},
{
"input": "10 7\n5 1 2 5 4 3 5 2 2 4",
"output": "8 9 10 1 3 4 5 6 7 "
},
{
"input": "10 109\n5 5 4 4 8 10 9 10 9 8",
"output": "-1"
},
{
"input": "20 430\n25 27 25 24 24 49 11 30 24 50 48 40 41 5 19 45 16 43 43 12",
"output": "12 13 16 18 19 2 6 8 10 11 "
},
{
"input": "20 314\n7 14 13 11 11 11 14 14 9 9 12 11 13 13 10 13 11 12 10 10",
"output": "-1"
},
{
"input": "20 252\n2 8 13 3 12 15 1 7 11 14 5 7 2 12 5 12 10 5 6 1",
"output": "-1"
},
{
"input": "20 329\n21 48 18 162 100 7 83 104 32 145 24 122 5 25 16 99 53 116 164 79",
"output": "16 17 18 19 20 1 2 4 5 7 8 9 10 11 12 14 "
},
{
"input": "50 892\n50 50 43 50 44 50 44 44 49 50 50 47 50 50 48 50 40 45 50 42 46 50 49 48 47 49 44 45 44 46 48 45 48 43 45 48 48 47 47 49 47 37 45 31 44 45 39 50 48 50",
"output": "43 44 45 46 47 48 49 50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 "
},
{
"input": "50 68\n12 6 15 15 7 4 1 18 11 2 3 4 9 6 8 2 6 10 1 2 16 10 22 28 23 2 17 33 3 3 5 1 5 6 5 5 2 6 2 10 2 14 1 24 12 12 4 4 2 10",
"output": "21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 37 38 39 40 41 42 44 45 46 47 48 49 50 1 2 3 4 5 6 8 9 11 12 13 14 15 17 18 "
},
{
"input": "50 224\n5 4 5 5 5 5 5 3 5 5 5 5 4 5 5 4 5 5 5 5 5 5 5 5 4 5 5 4 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4",
"output": "33 34 35 36 37 38 39 40 41 42 43 44 45 46 "
},
{
"input": "50 479\n15 64 28 16 6 4 28 3 20 55 4 43 48 21 23 75 2 42 14 6 51 27 50 7 26 13 5 12 7 36 19 3 11 1 9 1 6 23 12 7 19 24 25 19 11 11 42 15 14 40",
"output": "39 41 42 43 44 47 48 49 50 1 2 3 4 7 9 10 12 13 14 15 16 18 19 21 22 23 25 26 30 31 38 "
},
{
"input": "150 2476\n70 21 114 127 22 11 29 59 51 59 35 3 53 88 5 8 44 4 8 100 1 27 1 25 27 56 48 22 23 103 85 66 14 58 20 7 176 11 19 26 105 97 83 3 29 30 52 92 59 11 135 37 59 8 66 20 47 19 143 16 93 18 57 71 1 13 141 1 119 6 2 87 40 68 28 22 20 53 31 19 15 33 32 9 70 63 16 26 77 7 45 52 73 25 22 21 68 79 16 3 164 22 3 42 15 6 1 18 59 3 55 110 33 2 93 11 31 23 92 24 35 116 38 101 53 3 70 4 76 46 2 45 1 3 14 35 57 21 113 8 45 36 32 45 60 13 68 27 40 17",
"output": "26 27 28 29 30 31 32 34 37 40 41 42 43 45 46 47 48 49 51 52 53 55 57 59 61 63 64 67 69 72 73 74 75 76 78 79 82 83 85 86 88 89 91 92 93 94 95 96 97 98 101 102 104 109 111 112 113 115 117 118 119 120 121 122 123 124 125 127 129 130 132 136 137 138 139 141 142 143 144 145 147 148 149 1 3 4 5 7 8 9 10 11 13 14 17 20 22 24 25 "
}
] | 186 | 0 | 0 | 13,411 |
|
225 | Barcode | [
"dp",
"matrices"
] | null | null | You've got an *n*<=×<=*m* pixel picture. Each pixel can be white or black. Your task is to change the colors of as few pixels as possible to obtain a barcode picture.
A picture is a barcode if the following conditions are fulfilled:
- All pixels in each column are of the same color. - The width of each monochrome vertical line is at least *x* and at most *y* pixels. In other words, if we group all neighbouring columns of the pixels with equal color, the size of each group can not be less than *x* or greater than *y*. | The first line contains four space-separated integers *n*, *m*, *x* and *y* (1<=≤<=*n*,<=*m*,<=*x*,<=*y*<=≤<=1000; *x*<=≤<=*y*).
Then follow *n* lines, describing the original image. Each of these lines contains exactly *m* characters. Character "." represents a white pixel and "#" represents a black pixel. The picture description doesn't have any other characters besides "." and "#". | In the first line print the minimum number of pixels to repaint. It is guaranteed that the answer exists. | [
"6 5 1 2\n##.#.\n.###.\n###..\n#...#\n.##.#\n###..\n",
"2 5 1 1\n#####\n.....\n"
] | [
"11\n",
"5\n"
] | In the first test sample the picture after changing some colors can looks as follows:
In the second test sample the picture after changing some colors can looks as follows: | [
{
"input": "6 5 1 2\n##.#.\n.###.\n###..\n#...#\n.##.#\n###..",
"output": "11"
},
{
"input": "10 5 3 7\n.####\n###..\n##.##\n#..#.\n.#...\n#.##.\n.##..\n.#.##\n#.#..\n.#..#",
"output": "24"
},
{
"input": "6 3 1 4\n##.\n#..\n#..\n..#\n.#.\n#.#",
"output": "6"
},
{
"input": "5 10 4 16\n.#####....\n##..#..##.\n.#..##.#..\n##..#####.\n...#.##..#",
"output": "21"
},
{
"input": "5 4 1 4\n####\n..##\n##..\n..#.\n#..#",
"output": "8"
},
{
"input": "1 1 1 2\n.",
"output": "0"
},
{
"input": "3 44 2 18\n####..###.#.##........##...###.####.#.....##\n...#....##.###.###.##.#####.#######.#..#..#.\n#...#.####.#.##.#.#.#.....##.##..###.#....##",
"output": "39"
},
{
"input": "69 1 1 2\n#\n.\n#\n#\n.\n#\n#\n.\n.\n#\n.\n.\n#\n.\n#\n#\n.\n#\n#\n#\n#\n#\n.\n#\n.\n.\n#\n#\n#\n.\n.\n.\n.\n#\n#\n.\n#\n#\n.\n#\n.\n.\n#\n.\n.\n.\n#\n.\n.\n#\n#\n.\n.\n#\n.\n.\n.\n#\n#\n#\n#\n#\n.\n#\n.\n#\n#\n#\n#",
"output": "31"
},
{
"input": "56 2 2 2\n##\n##\n##\n..\n..\n##\n.#\n#.\n..\n##\n##\n..\n..\n#.\n#.\n#.\n#.\n##\n..\n.#\n..\n##\n##\n.#\n#.\n.#\n..\n..\n#.\n..\n##\n..\n#.\n.#\n#.\n#.\n#.\n##\n#.\n##\n##\n.#\n#.\n##\n..\n.#\n#.\n#.\n##\n..\n..\n#.\n##\n..\n..\n##",
"output": "55"
}
] | 92 | 512,000 | 0 | 13,412 |
|
0 | none | [
"none"
] | null | null | Codeforces is a wonderful platform and one its feature shows how much someone contributes to the community. Every registered user has contribution — an integer number, not necessarily positive. There are *n* registered users and the *i*-th of them has contribution *t**i*.
Limak is a little polar bear and he's new into competitive programming. He doesn't even have an account in Codeforces but he is able to upvote existing blogs and comments. We assume that every registered user has infinitely many blogs and comments.
- Limak can spend *b* minutes to read one blog and upvote it. Author's contribution will be increased by 5. - Limak can spend *c* minutes to read one comment and upvote it. Author's contribution will be increased by 1.
Note that it's possible that Limak reads blogs faster than comments.
Limak likes ties. He thinks it would be awesome to see a tie between at least *k* registered users. To make it happen he is going to spend some time on reading and upvoting. After that, there should exist an integer value *x* that at least *k* registered users have contribution exactly *x*.
How much time does Limak need to achieve his goal? | The first line contains four integers *n*, *k*, *b* and *c* (2<=≤<=*k*<=≤<=*n*<=≤<=200<=000,<=1<=≤<=*b*,<=*c*<=≤<=1000) — the number of registered users, the required minimum number of users with the same contribution, time needed to read and upvote a blog, and time needed to read and upvote a comment, respectively.
The second line contains *n* integers *t*1,<=*t*2,<=...,<=*t**n* (|*t**i*|<=≤<=109) where *t**i* denotes contribution of the *i*-th registered user. | Print the minimum number of minutes Limak will spend to get a tie between at least *k* registered users. | [
"4 3 100 30\n12 2 6 1\n",
"4 3 30 100\n12 2 6 1\n",
"6 2 987 789\n-8 42 -4 -65 -8 -8\n"
] | [
"220\n",
"190\n",
"0\n"
] | In the first sample, there are 4 registered users and Limak wants a tie between at least 3 of them. Limak should behave as follows.
- He spends 100 minutes to read one blog of the 4-th user and increase his contribution from 1 to 6. - Then he spends 4·30 = 120 minutes to read four comments of the 2-nd user and increase his contribution from 2 to 6 (four times it was increaded by 1).
In the given scenario, Limak spends 100 + 4·30 = 220 minutes and after that each of users 2, 3, 4 has contribution 6.
In the second sample, Limak needs 30 minutes to read a blog and 100 minutes to read a comment. This time he can get 3 users with contribution equal to 12 by spending 100 + 3·30 = 190 minutes:
- Spend 2·30 = 60 minutes to read two blogs of the 1-st user to increase his contribution from 2 to 12. - Spend 30 + 100 minutes to read one blog and one comment of the 3-rd user. His contribution will change from 6 to 6 + 5 + 1 = 12. | [
{
"input": "4 3 100 30\n12 2 6 1",
"output": "220"
},
{
"input": "4 3 30 100\n12 2 6 1",
"output": "190"
},
{
"input": "6 2 987 789\n-8 42 -4 -65 -8 -8",
"output": "0"
},
{
"input": "5 5 1 1000\n1 1 1 1 2",
"output": "4000"
},
{
"input": "6 6 1 1000\n1 1 1 1 1 2",
"output": "4005"
},
{
"input": "2 2 1 1\n0 0",
"output": "0"
},
{
"input": "8 7 3 10\n-35 -33 10 15 20 25 30 31",
"output": "127"
},
{
"input": "2 2 1000 1\n101 1",
"output": "100"
},
{
"input": "100 20 62 96\n15 40 73 97 25 33 45 62 30 68 72 80 29 29 57 29 93 55 26 11 71 54 74 87 88 17 95 26 37 85 77 40 68 68 13 56 34 3 43 21 63 84 73 4 100 5 90 55 97 7 83 56 11 80 86 24 100 90 49 25 94 9 87 17 25 85 64 8 73 37 49 85 7 58 61 14 21 6 86 23 65 53 56 71 83 11 88 63 92 36 43 13 83 82 53 75 24 91 59 49",
"output": "3300"
},
{
"input": "100 20 92 70\n97 49 30 24 17 21 66 52 80 53 35 79 47 24 48 64 3 35 83 39 28 68 48 62 30 73 66 36 87 46 38 26 31 72 97 92 1 24 84 83 39 33 67 72 82 33 93 52 34 55 38 36 4 9 45 82 5 42 88 50 26 80 62 15 101 27 28 36 6 39 56 80 85 20 87 60 10 34 5 26 52 44 67 15 14 80 46 13 16 7 16 72 29 14 78 20 29 52 33 80",
"output": "3060"
},
{
"input": "100 20 97 94\n75 9 49 36 54 44 4 70 60 11 16 78 31 82 95 98 69 23 42 23 85 95 77 53 9 5 42 8 61 48 47 25 98 76 16 96 28 46 55 2 37 54 88 40 13 53 33 100 76 53 1 12 56 18 32 11 76 80 76 61 100 61 102 6 25 85 80 63 16 29 34 61 53 55 91 78 23 65 58 81 54 40 6 73 88 49 100 14 100 22 76 53 20 67 43 51 88 58 29 97",
"output": "3914"
},
{
"input": "100 20 76 94\n76 47 15 63 81 65 66 37 42 3 80 44 89 16 22 89 67 46 64 85 2 27 57 43 38 66 5 65 40 33 100 58 12 83 10 24 58 85 75 69 86 79 51 103 31 35 8 25 87 66 73 25 5 1 46 4 58 47 39 70 79 90 59 45 31 48 93 16 24 10 69 37 44 78 28 91 101 43 33 35 71 20 86 2 75 7 55 13 52 70 45 20 93 37 87 9 71 60 31 7",
"output": "4102"
},
{
"input": "100 20 79 68\n67 30 14 87 76 58 62 66 15 58 65 92 40 59 84 22 66 55 19 43 23 51 99 11 33 74 72 34 29 88 73 94 99 47 7 100 15 69 34 99 91 20 44 95 51 42 99 56 79 39 35 56 52 57 10 97 4 10 35 13 41 49 44 28 70 69 23 33 6 6 36 5 59 36 78 27 16 29 90 90 71 83 3 63 69 92 64 80 97 73 28 41 24 71 94 99 92 65 15 104",
"output": "3359"
},
{
"input": "100 20 59 93\n30 70 83 91 93 68 89 79 52 93 15 74 6 99 86 17 79 28 71 55 50 38 27 6 80 81 5 86 56 23 24 104 27 22 73 32 72 28 22 48 36 9 92 101 10 1 27 93 90 81 12 91 82 96 56 13 46 101 66 86 21 83 34 69 86 37 103 76 93 98 44 13 104 5 39 36 84 53 23 102 63 62 57 28 103 90 73 17 64 29 76 87 102 91 21 6 21 69 36 23",
"output": "2793"
},
{
"input": "100 20 63 93\n43 59 53 73 21 33 77 80 19 69 73 5 98 92 7 97 18 7 95 58 7 12 102 70 10 84 91 5 69 105 95 53 32 23 30 20 32 75 39 72 69 80 105 42 92 2 64 98 80 38 57 52 33 98 2 49 35 51 29 95 51 83 4 31 80 21 61 16 31 58 94 43 77 5 106 74 80 87 36 102 71 89 98 86 92 74 22 90 71 11 99 54 51 55 52 91 84 105 99 42",
"output": "3498"
},
{
"input": "100 20 93 67\n25 26 15 22 31 45 1 9 46 68 103 72 45 42 48 68 17 60 35 63 31 74 59 4 35 70 80 3 84 93 21 63 86 50 37 54 52 58 24 95 99 12 29 43 59 35 79 80 45 1 29 106 16 94 47 97 65 68 81 3 14 10 21 84 56 52 53 5 32 4 43 88 7 28 95 18 1 62 27 104 78 7 94 23 8 98 8 65 42 45 50 79 2 105 31 26 90 94 64 67",
"output": "4201"
},
{
"input": "100 20 72 92\n27 36 39 6 70 31 35 26 67 108 90 1 3 17 3 80 27 71 100 56 51 5 52 80 95 42 14 49 6 23 96 52 50 98 21 84 81 76 24 65 83 76 18 22 22 42 73 92 104 50 103 25 77 10 79 34 91 71 84 41 20 4 92 107 15 102 66 67 87 98 108 41 70 86 82 4 36 49 33 82 38 54 50 18 19 45 80 80 74 38 58 46 1 59 46 47 44 30 34 103",
"output": "3936"
},
{
"input": "100 20 77 91\n81 92 92 100 28 46 72 8 91 7 108 90 31 21 87 41 39 43 22 106 32 64 82 87 106 59 43 28 11 49 84 81 78 69 22 86 93 30 27 23 76 54 26 96 84 13 94 107 103 106 37 49 35 104 88 78 9 73 97 79 66 86 32 66 31 64 72 73 51 46 62 15 104 14 78 48 11 43 51 74 23 31 50 55 84 43 4 38 61 23 57 82 93 94 99 18 80 9 72 23",
"output": "3948"
},
{
"input": "100 20 81 98\n99 2 93 108 49 18 54 55 50 75 14 23 39 67 91 25 55 82 71 43 51 66 36 50 99 18 34 48 93 80 78 28 18 93 110 67 73 66 104 15 90 103 36 53 56 38 3 50 4 17 38 58 13 73 58 67 96 6 108 29 54 30 84 58 95 34 82 105 78 39 21 46 28 74 5 67 30 11 66 88 101 13 3 44 77 32 97 31 94 30 103 84 14 13 49 89 14 86 31 48",
"output": "4454"
}
] | 62 | 0 | 0 | 13,432 |
|
842 | Vitya and Strange Lesson | [
"binary search",
"data structures"
] | null | null | Today at the lesson Vitya learned a very interesting function — mex. Mex of a sequence of numbers is the minimum non-negative number that is not present in the sequence as element. For example, *mex*([4,<=33,<=0,<=1,<=1,<=5])<==<=2 and *mex*([1,<=2,<=3])<==<=0.
Vitya quickly understood all tasks of the teacher, but can you do the same?
You are given an array consisting of *n* non-negative integers, and *m* queries. Each query is characterized by one number *x* and consists of the following consecutive steps:
- Perform the bitwise addition operation modulo 2 (xor) of each array element with the number *x*. - Find mex of the resulting array.
Note that after each query the array changes. | First line contains two integer numbers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=3·105) — number of elements in array and number of queries.
Next line contains *n* integer numbers *a**i* (0<=≤<=*a**i*<=≤<=3·105) — elements of then array.
Each of next *m* lines contains query — one integer number *x* (0<=≤<=*x*<=≤<=3·105). | For each query print the answer on a separate line. | [
"2 2\n1 3\n1\n3\n",
"4 3\n0 1 5 6\n1\n2\n4\n",
"5 4\n0 1 5 6 7\n1\n1\n4\n5\n"
] | [
"1\n0\n",
"2\n0\n0\n",
"2\n2\n0\n2\n"
] | none | [
{
"input": "2 2\n1 3\n1\n3",
"output": "1\n0"
},
{
"input": "4 3\n0 1 5 6\n1\n2\n4",
"output": "2\n0\n0"
},
{
"input": "5 4\n0 1 5 6 7\n1\n1\n4\n5",
"output": "2\n2\n0\n2"
},
{
"input": "5 5\n1 2 3 4 5\n1\n2\n3\n4\n5",
"output": "1\n3\n0\n2\n1"
},
{
"input": "9 3\n2 3 4 5 6 7 8 9 10\n1\n2\n3",
"output": "0\n2\n0"
},
{
"input": "10 30\n0 0 0 0 0 0 0 0 0 0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0",
"output": "1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1"
},
{
"input": "17 30\n4194 1990 2257 1363 2798 386 3311 3152 1808 1453 3874 4388 1268 3924 3799 1269 968\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8\n8",
"output": "0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0"
}
] | 2,000 | 20,275,200 | 0 | 13,439 |
|
999 | Equalize the Remainders | [
"data structures",
"greedy",
"implementation"
] | null | null | You are given an array consisting of $n$ integers $a_1, a_2, \dots, a_n$, and a positive integer $m$. It is guaranteed that $m$ is a divisor of $n$.
In a single move, you can choose any position $i$ between $1$ and $n$ and increase $a_i$ by $1$.
Let's calculate $c_r$ ($0 \le r \le m-1)$ — the number of elements having remainder $r$ when divided by $m$. In other words, for each remainder, let's find the number of corresponding elements in $a$ with that remainder.
Your task is to change the array in such a way that $c_0 = c_1 = \dots = c_{m-1} = \frac{n}{m}$.
Find the minimum number of moves to satisfy the above requirement. | The first line of input contains two integers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5, 1 \le m \le n$). It is guaranteed that $m$ is a divisor of $n$.
The second line of input contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^9$), the elements of the array. | In the first line, print a single integer — the minimum number of moves required to satisfy the following condition: for each remainder from $0$ to $m - 1$, the number of elements of the array having this remainder equals $\frac{n}{m}$.
In the second line, print any array satisfying the condition and can be obtained from the given array with the minimum number of moves. The values of the elements of the resulting array must not exceed $10^{18}$. | [
"6 3\n3 2 0 6 10 12\n",
"4 2\n0 1 2 3\n"
] | [
"3\n3 2 0 7 10 14 \n",
"0\n0 1 2 3 \n"
] | none | [
{
"input": "6 3\n3 2 0 6 10 12",
"output": "3\n3 2 0 7 10 14 "
},
{
"input": "4 2\n0 1 2 3",
"output": "0\n0 1 2 3 "
},
{
"input": "1 1\n1000000000",
"output": "0\n1000000000 "
},
{
"input": "6 3\n3 2 0 6 10 11",
"output": "1\n3 2 0 7 10 11 "
},
{
"input": "100 25\n6745 2075 7499 7517 1776 5164 2335 2745 4465 1457 7565 2232 2486 9025 8059 9646 8017 7662 9690 3352 2306 366 7422 1073 7169 8966 4506 8225 5614 8628 2908 7452 9625 9332 7097 353 1043 8118 5794 4486 626 971 6731 6618 887 6354 4814 7307 7681 6160 9351 2579 411 3436 5570 2812 2726 4433 3220 577 5891 3861 528 2183 127 5579 6979 4005 9953 5038 9937 4792 3003 9417 8796 1565 11 2596 2486 3494 4464 9568 5512 5565 9822 9820 4848 2889 9527 2249 9860 8236 256 8434 8038 6407 5570 5922 7435 2815",
"output": "88\n6745 2075 7499 7517 1776 5164 2335 2745 4465 1457 7565 2232 2486 9025 8059 9646 8017 7662 9690 3352 2306 366 7422 1073 7169 8966 4506 8225 5614 8628 2908 7452 9625 9332 7097 353 1043 8118 5794 4486 626 971 6731 6618 887 6354 4814 7307 7681 6160 9351 2579 411 3436 5570 2812 2726 4433 3220 577 5891 3863 528 2183 127 5579 6979 4005 9953 5038 9937 4792 3005 9417 8796 1565 24 2596 2505 3494 4464 9568 5513 5566 9822 9823 4848 2899 9530 2249 9860 8259 259 8434 8038 6408 5573 5922 7435 2819 "
}
] | 780 | 29,491,200 | 3 | 13,457 |
|
712 | Memory and Scores | [
"combinatorics",
"dp",
"math"
] | null | null | Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score *a* and Lexa starts with score *b*. In a single turn, both Memory and Lexa get some integer in the range [<=-<=*k*;*k*] (i.e. one integer among <=-<=*k*,<=<=-<=*k*<=+<=1,<=<=-<=*k*<=+<=2,<=...,<=<=-<=2,<=<=-<=1,<=0,<=1,<=2,<=...,<=*k*<=-<=1,<=*k*) and add them to their current scores. The game has exactly *t* turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.
Memory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2*k*<=+<=1)2*t* games in total. Since the answer can be very large, you should print it modulo 109<=+<=7. Please solve this problem for Memory. | The first and only line of input contains the four integers *a*, *b*, *k*, and *t* (1<=≤<=*a*,<=*b*<=≤<=100, 1<=≤<=*k*<=≤<=1000, 1<=≤<=*t*<=≤<=100) — the amount Memory and Lexa start with, the number *k*, and the number of turns respectively. | Print the number of possible games satisfying the conditions modulo 1<=000<=000<=007 (109<=+<=7) in one line. | [
"1 2 2 1\n",
"1 1 1 2\n",
"2 12 3 1\n"
] | [
"6\n",
"31\n",
"0\n"
] | In the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins. | [
{
"input": "1 2 2 1",
"output": "6"
},
{
"input": "1 1 1 2",
"output": "31"
},
{
"input": "2 12 3 1",
"output": "0"
},
{
"input": "4 6 2 1",
"output": "3"
},
{
"input": "4 6 2 2",
"output": "122"
},
{
"input": "6 4 2 2",
"output": "435"
},
{
"input": "10 1 3 3",
"output": "112812"
},
{
"input": "5 3 1 1",
"output": "8"
},
{
"input": "50 22 5 5",
"output": "876439301"
},
{
"input": "6 20 1 1",
"output": "0"
},
{
"input": "42 42 2 3",
"output": "6937"
},
{
"input": "42 42 3 2",
"output": "1085"
},
{
"input": "45 54 4 5",
"output": "433203628"
},
{
"input": "6 5 4 3",
"output": "282051"
},
{
"input": "42 42 42 42",
"output": "284470145"
},
{
"input": "1 100 42 42",
"output": "58785421"
},
{
"input": "1 100 1000 100",
"output": "542673827"
},
{
"input": "1 1 1000 100",
"output": "922257788"
},
{
"input": "100 100 1000 100",
"output": "922257788"
},
{
"input": "1 8 1 4",
"output": "1"
},
{
"input": "9 4 5 2",
"output": "11045"
},
{
"input": "2 6 6 2",
"output": "8015"
},
{
"input": "7 8 5 9",
"output": "860378382"
},
{
"input": "3 7 8 6",
"output": "510324293"
},
{
"input": "69 69 803 81",
"output": "74925054"
},
{
"input": "67 67 871 88",
"output": "123371511"
},
{
"input": "71 71 891 31",
"output": "790044038"
},
{
"input": "49 49 631 34",
"output": "764129060"
},
{
"input": "83 83 770 49",
"output": "761730117"
},
{
"input": "49 49 163 15",
"output": "458364105"
},
{
"input": "38 38 701 74",
"output": "496603581"
},
{
"input": "65 65 803 79",
"output": "253679300"
},
{
"input": "56 56 725 64",
"output": "338598412"
},
{
"input": "70 70 176 56",
"output": "990579000"
},
{
"input": "32 32 44 79",
"output": "20803934"
},
{
"input": "35 35 353 21",
"output": "149936279"
},
{
"input": "57 57 896 52",
"output": "271910130"
},
{
"input": "86 86 373 19",
"output": "940701970"
},
{
"input": "27 27 296 97",
"output": "394599845"
},
{
"input": "60 60 86 51",
"output": "277883413"
},
{
"input": "40 40 955 95",
"output": "600387428"
},
{
"input": "34 34 706 59",
"output": "274236101"
},
{
"input": "74 74 791 51",
"output": "367968499"
},
{
"input": "69 69 443 53",
"output": "385620893"
},
{
"input": "59 19 370 48",
"output": "125206836"
},
{
"input": "78 82 511 33",
"output": "375900871"
},
{
"input": "66 90 805 16",
"output": "593436252"
},
{
"input": "60 61 772 19",
"output": "931528755"
},
{
"input": "81 13 607 21",
"output": "762608093"
},
{
"input": "35 79 128 21",
"output": "177972209"
},
{
"input": "93 25 958 20",
"output": "873170266"
},
{
"input": "44 85 206 80",
"output": "170080402"
},
{
"input": "79 99 506 18",
"output": "486170430"
},
{
"input": "97 22 29 8",
"output": "471632954"
},
{
"input": "14 47 184 49",
"output": "726421144"
},
{
"input": "74 33 868 5",
"output": "826980486"
},
{
"input": "53 79 823 11",
"output": "526626321"
},
{
"input": "99 99 913 42",
"output": "446683872"
},
{
"input": "52 34 89 41",
"output": "905639400"
},
{
"input": "87 100 200 80",
"output": "913761305"
},
{
"input": "40 94 510 53",
"output": "233079261"
},
{
"input": "2 56 438 41",
"output": "500592304"
},
{
"input": "6 68 958 41",
"output": "719351710"
},
{
"input": "44 80 814 26",
"output": "414148151"
},
{
"input": "100 1 1000 100",
"output": "603336175"
},
{
"input": "1 3 1000 100",
"output": "604187087"
},
{
"input": "10 10 1000 100",
"output": "922257788"
}
] | 2,000 | 11,673,600 | 0 | 13,499 |
|
51 | Caterpillar | [
"dfs and similar",
"dp",
"graphs",
"trees"
] | F. Caterpillar | 2 | 256 | An undirected graph is called a caterpillar if it is a connected graph without cycles and it has such a path *p* that any vertex is located at a distance of at most 1 from the path *p*. The caterpillar can contain loops (edges from a vertex to itself) but cannot contain multiple (parallel) edges.
The picture contains an example of a caterpillar:
You are given an undirected graph *G*. You are allowed to do a merging operations, each such operation merges two vertices into one vertex. For that two any vertices *a* and *b* (*a*<=≠<=*b*) are chosen. These verteces are deleted together with their edges (which are incident to at least one of the vertices *a* or *b*) but a new vertex *w* is added together with edges (*x*,<=*w*) for each edge (*a*,<=*w*) and/or (*b*,<=*w*). If there was the edge (*a*,<=*b*) it transforms to the loop (*w*,<=*w*). The resulting graph (after the merging operation) may contain multiple (parallel) edges between pairs of vertices and loops. Let us note that this operation decreases the number of vertices of graph by 1 but leaves the number of edges in the graph unchanged.
The merging operation can be informally described as a unity of two vertices of the graph into one with the natural transformation of the graph edges.
You may apply this operation consecutively and make the given graph to be a caterpillar. Write a program that will print the minimal number of merging operations required to make the given graph a caterpillar. | The first line contains a pair of integers *n*, *m* (1<=≤<=*n*<=≤<=2000;0<=≤<=*m*<=≤<=105), where *n* represents the number of vertices in the graph and *m* is the number of edges in it. Then the following *m* lines contain edge descriptions, one edge description per line. Every line contains a pair of integers *a**i*,<=*b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*;*a**i*<=≠<=*b**i*), *a**i*,<=*b**i* which represent the indices of the vertices connected by the edge. The vertices are numbered from 1 to *n*. In the given graph it will be no more than one edge between any pair of vertices. The given graph is not necessarily connected. | Print the minimal required number of operations. | [
"4 4\n1 2\n2 3\n3 4\n4 2\n",
"6 3\n1 2\n3 4\n5 6\n",
"7 6\n1 2\n2 3\n1 4\n4 5\n1 6\n6 7\n"
] | [
"2\n",
"2\n",
"1\n"
] | none | [] | 92 | 0 | 0 | 13,514 |
577 | Modulo Sum | [
"combinatorics",
"data structures",
"dp",
"two pointers"
] | null | null | You are given a sequence of numbers *a*1,<=*a*2,<=...,<=*a**n*, and a number *m*.
Check if it is possible to choose a non-empty subsequence *a**i**j* such that the sum of numbers in this subsequence is divisible by *m*. | The first line contains two numbers, *n* and *m* (1<=≤<=*n*<=≤<=106, 2<=≤<=*m*<=≤<=103) — the size of the original sequence and the number such that sum should be divisible by it.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=109). | In the single line print either "YES" (without the quotes) if there exists the sought subsequence, or "NO" (without the quotes), if such subsequence doesn't exist. | [
"3 5\n1 2 3\n",
"1 6\n5\n",
"4 6\n3 1 1 3\n",
"6 6\n5 5 5 5 5 5\n"
] | [
"YES\n",
"NO\n",
"YES\n",
"YES\n"
] | In the first sample test you can choose numbers 2 and 3, the sum of which is divisible by 5.
In the second sample test the single non-empty subsequence of numbers is a single number 5. Number 5 is not divisible by 6, that is, the sought subsequence doesn't exist.
In the third sample test you need to choose two numbers 3 on the ends.
In the fourth sample test you can take the whole subsequence. | [
{
"input": "3 5\n1 2 3",
"output": "YES"
},
{
"input": "1 6\n5",
"output": "NO"
},
{
"input": "4 6\n3 1 1 3",
"output": "YES"
},
{
"input": "6 6\n5 5 5 5 5 5",
"output": "YES"
},
{
"input": "4 5\n1 1 1 1",
"output": "NO"
},
{
"input": "5 5\n1 1 1 1 1",
"output": "YES"
},
{
"input": "4 7\n1 2 3 3",
"output": "YES"
},
{
"input": "1 47\n0",
"output": "YES"
},
{
"input": "2 47\n1 0",
"output": "YES"
},
{
"input": "9 11\n8 8 8 8 8 8 8 8 5",
"output": "NO"
},
{
"input": "10 11\n8 8 8 8 8 8 8 8 7 8",
"output": "YES"
},
{
"input": "3 5\n2 1 3",
"output": "YES"
},
{
"input": "100 968\n966 966 967 966 967 967 967 967 966 966 966 967 966 966 966 967 967 966 966 967 967 967 967 966 967 967 967 967 563 967 967 967 600 967 967 966 967 966 967 966 967 966 967 966 966 966 967 966 967 966 966 967 967 193 966 966 967 966 967 967 967 966 967 966 966 580 966 967 966 966 967 966 966 966 967 967 967 967 966 967 967 966 966 966 967 967 966 966 967 966 966 966 967 966 966 967 966 967 966 966",
"output": "YES"
},
{
"input": "100 951\n950 949 949 949 949 950 950 949 949 950 950 949 949 949 496 949 950 949 950 159 950 949 949 950 950 949 950 949 949 950 949 950 949 949 950 949 950 950 950 950 949 949 949 949 949 950 950 950 950 950 950 950 949 950 949 949 950 949 950 950 949 950 950 950 949 950 949 950 950 950 950 949 949 950 950 949 950 950 950 950 949 950 950 949 949 635 612 949 949 949 949 949 949 949 950 949 949 950 949 950",
"output": "YES"
},
{
"input": "100 940\n1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 2 2 1 1 1 2 2 2 2 1 1 1 1 2 2 1 403 2 2 1 1 1 2 2 2 1 2 2 1 1 2 2 1 1 1 1 2 1 2 691 1 2 1 1 1 1 1 2 2 2 2 2 1 2 1 1 1 1 1 1 2 2 1 2 2 1 1 1 2 1 2 1 1 2 2 1 1 2 786 1",
"output": "YES"
},
{
"input": "100 917\n2 1 2 2 2 1 1 2 2 2 1 1 1 2 1 2 2 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 1 1 1 2 1 2 340 2 399 2 1 2 2 2 2 178 1 1 2 1 1 1 2 2 1 2 2 2 1 2 1 1 1 1 1 1 2 1 1 1 2 2 1 1 2 2 2 1 2 2 2 2 1 2 1 2 2 2 2 2 1 1 2 2 2 2",
"output": "YES"
},
{
"input": "1 2\n1000000000",
"output": "YES"
}
] | 0 | 0 | -1 | 13,529 |
|
917 | The Monster | [
"dp",
"greedy",
"implementation",
"math"
] | null | null | As Will is stuck in the Upside Down, he can still communicate with his mom, Joyce, through the Christmas lights (he can turn them on and off with his mind). He can't directly tell his mom where he is, because the monster that took him to the Upside Down will know and relocate him.
Thus, he came up with a puzzle to tell his mom his coordinates. His coordinates are the answer to the following problem.
A string consisting only of parentheses ('(' and ')') is called a bracket sequence. Some bracket sequence are called correct bracket sequences. More formally:
- Empty string is a correct bracket sequence. - if *s* is a correct bracket sequence, then (*s*) is also a correct bracket sequence. - if *s* and *t* are correct bracket sequences, then *st* (concatenation of *s* and *t*) is also a correct bracket sequence.
A string consisting of parentheses and question marks ('?') is called pretty if and only if there's a way to replace each question mark with either '(' or ')' such that the resulting string is a non-empty correct bracket sequence.
Will gave his mom a string *s* consisting of parentheses and question marks (using Morse code through the lights) and his coordinates are the number of pairs of integers (*l*,<=*r*) such that 1<=≤<=*l*<=≤<=*r*<=≤<=|*s*| and the string *s**l**s**l*<=+<=1... *s**r* is pretty, where *s**i* is *i*-th character of *s*.
Joyce doesn't know anything about bracket sequences, so she asked for your help. | The first and only line of input contains string *s*, consisting only of characters '(', ')' and '?' (2<=≤<=|*s*|<=≤<=5000). | Print the answer to Will's puzzle in the first and only line of output. | [
"((?))\n",
"??()??\n"
] | [
"4\n",
"7\n"
] | For the first sample testcase, the pretty substrings of *s* are:
1. "(?" which can be transformed to "()". 1. "?)" which can be transformed to "()". 1. "((?)" which can be transformed to "(())". 1. "(?))" which can be transformed to "(())".
For the second sample testcase, the pretty substrings of *s* are:
1. "??" which can be transformed to "()". 1. "()". 1. "??()" which can be transformed to "()()". 1. "?()?" which can be transformed to "(())". 1. "??" which can be transformed to "()". 1. "()??" which can be transformed to "()()". 1. "??()??" which can be transformed to "()()()". | [
{
"input": "((?))",
"output": "4"
},
{
"input": "??()??",
"output": "7"
},
{
"input": "?????)(???",
"output": "21"
},
{
"input": "()()((?(()(((()()(())(((()((())))(()))(()(((((())))()))(((()()()))))))(((((()))))))))",
"output": "62"
},
{
"input": "))((()(()((((()))())()())((())())(((()()(())))))((())()()(()()(())()))()()(()()()(((()(()(()(()))))(",
"output": "88"
},
{
"input": "????????????????????????????????????????????????????????????????????????????????????????????????????",
"output": "2500"
},
{
"input": ")(",
"output": "0"
},
{
"input": "?(",
"output": "0"
},
{
"input": "??",
"output": "1"
},
{
"input": ")?(??((???????()?(?????????)??(????????((?)?????)????)??????(?????)?)?????)??????(??()??????)????????)?)()??????????????())????????(???)??)????????????????????(?????)??)???)??(???????????????)???)??)?",
"output": "8314"
},
{
"input": "()",
"output": "1"
},
{
"input": "(?",
"output": "1"
}
] | 46 | 0 | 0 | 13,533 |
|
590 | Three States | [
"dfs and similar",
"graphs",
"shortest paths"
] | null | null | The famous global economic crisis is approaching rapidly, so the states of Berman, Berance and Bertaly formed an alliance and allowed the residents of all member states to freely pass through the territory of any of them. In addition, it was decided that a road between the states should be built to guarantee so that one could any point of any country can be reached from any point of any other State.
Since roads are always expensive, the governments of the states of the newly formed alliance asked you to help them assess the costs. To do this, you have been issued a map that can be represented as a rectangle table consisting of *n* rows and *m* columns. Any cell of the map either belongs to one of three states, or is an area where it is allowed to build a road, or is an area where the construction of the road is not allowed. A cell is called passable, if it belongs to one of the states, or the road was built in this cell. From any passable cells you can move up, down, right and left, if the cell that corresponds to the movement exists and is passable.
Your task is to construct a road inside a minimum number of cells, so that it would be possible to get from any cell of any state to any cell of any other state using only passable cells.
It is guaranteed that initially it is possible to reach any cell of any state from any cell of this state, moving only along its cells. It is also guaranteed that for any state there is at least one cell that belongs to it. | The first line of the input contains the dimensions of the map *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=1000) — the number of rows and columns respectively.
Each of the next *n* lines contain *m* characters, describing the rows of the map. Digits from 1 to 3 represent the accessory to the corresponding state. The character '.' corresponds to the cell where it is allowed to build a road and the character '#' means no construction is allowed in this cell. | Print a single integer — the minimum number of cells you need to build a road inside in order to connect all the cells of all states. If such a goal is unachievable, print -1. | [
"4 5\n11..2\n#..22\n#.323\n.#333",
"1 5\n1#2#3\n"
] | [
"2",
"-1\n"
] | none | [
{
"input": "4 5\n11..2\n#..22\n#.323\n.#333",
"output": "2"
},
{
"input": "1 5\n1#2#3",
"output": "-1"
},
{
"input": "3 4\n.2..\n...3\n.1#.",
"output": "2"
},
{
"input": "10 10\n##.#..#.#2\n...###....\n#..#....##\n.....#....\n.#........\n.....#####\n...#..#...\n....###...\n###.##...#\n.#...1#.3.",
"output": "-1"
},
{
"input": "4 3\n..#\n.3.\n..2\n..1",
"output": "1"
},
{
"input": "5 5\n.2...\n#2.3.\n.#..#\n.#.11\n#..#.",
"output": "2"
},
{
"input": "1 3\n231",
"output": "0"
},
{
"input": "3 1\n3\n1\n2",
"output": "0"
},
{
"input": "1 4\n12#3",
"output": "-1"
},
{
"input": "10 10\n#...33.#.#\n#.#.33.#1.\n2.....#.11\n222#.#.#..\n####...#.#\n#.........\n.#....#...\n..#..#.##.\n##.....#.#\n#..#....#.",
"output": "12"
},
{
"input": "10 10\n..#.....#.\n.#.##...#.\n..#.......\n..111.....\n#..#.....#\n.#...2....\n.....2....\n.....222..\n..........\n#.3....#..",
"output": "6"
},
{
"input": "10 10\n##.#.##.##\n#.#..####.\n#.###.333.\n..#..#3.2#\n...###3..#\n..#.#..#.#\n...#.#.#..\n...##.1..#\n.##.#.1#.#\n..#.#.11..",
"output": "2"
},
{
"input": "10 10\n###..#.#.#\n#....####.\n##1###.#.#\n#.11######\n##11#####.\n..#####..#\n####...#.3\n.#.#..2223\n#####..#33\n#.########",
"output": "-1"
},
{
"input": "3 10\n........2.\n......1...\n.........3",
"output": "3"
},
{
"input": "10 10\n1111.22222\n1111.22222\n11......22\n11......22\n..........\n3333333333\n3333333333\n3333333333\n3333333333\n3333333333",
"output": "2"
},
{
"input": "4 4\n3###\n.222\n.#.2\n1222",
"output": "1"
},
{
"input": "3 3\n##3\n1..\n222",
"output": "1"
},
{
"input": "4 4\n1...\n.222\n....\n...3",
"output": "2"
},
{
"input": "1 9\n111222333",
"output": "0"
},
{
"input": "1 10\n111222333.",
"output": "0"
},
{
"input": "1 15\n111112222233333",
"output": "0"
},
{
"input": "5 4\n2..3\n2..3\n....\n1..1\n1111",
"output": "2"
},
{
"input": "10 1\n1\n.\n2\n2\n2\n2\n2\n.\n3\n.",
"output": "2"
},
{
"input": "3 3\n#2#\n1.3\n1.#",
"output": "1"
},
{
"input": "1 9\n1.22222.3",
"output": "2"
},
{
"input": "3 3\n1.2\n1.2\n333",
"output": "0"
},
{
"input": "4 7\n2..1..3\n2##.##3\n2##.##3\n2.....3",
"output": "4"
}
] | 1,762 | 100,556,800 | 3 | 13,560 |
|
523 | Name Quest | [
"*special",
"greedy"
] | null | null | A Martian boy is named *s* — he has got this name quite recently from his parents for his coming of age birthday. Now he enjoys looking for his name everywhere. If he sees that he can obtain his name from some string by removing zero or more letters (at that, the remaining letters remain in the same order), he gets happy. For example, if *s*=«aba», then strings «baobab», «aabbaa», «helloabahello» make him very happy and strings «aab», «baaa» and «helloabhello» do not.
However rather than being happy once, he loves twice as much being happy twice! So, when he got string *t* as a present, he wanted to cut it in two parts (the left part and the right part) so that each part made him happy.
Help *s* determine the number of distinct ways to cut the given string *t* into two parts in the required manner. | The first line contains string *s*, consisting of lowercase English letters. The length of string *s* is from 1 to 1000 letters.
The second line contains string *t*, that also consists of lowercase English letters. The length of string *t* is from 1 to 106 letters. | Print the sought number of ways to cut string *t* in two so that each part made *s* happy. | [
"aba\nbaobababbah\n",
"mars\nsunvenusearthmarsjupitersaturnuranusneptune\n"
] | [
"2\n",
"0\n"
] | none | [
{
"input": "aba\nbaobababbah",
"output": "2"
},
{
"input": "mars\nsunvenusearthmarsjupitersaturnuranusneptune",
"output": "0"
},
{
"input": "rry\nsorrymercuryismissedabove",
"output": "3"
},
{
"input": "a\naaaaaaaaaaaaaa",
"output": "13"
},
{
"input": "abcaba\nabcabaabcabaabcabaabcaba",
"output": "13"
},
{
"input": "lol\nlol",
"output": "0"
},
{
"input": "aaaaaaaaaaaa\naaaaaa",
"output": "0"
},
{
"input": "a\na",
"output": "0"
}
] | 77 | 3,379,200 | 3 | 13,561 |
|
864 | Cities Excursions | [
"dfs and similar",
"graphs",
"trees"
] | null | null | There are *n* cities in Berland. Some pairs of them are connected with *m* directed roads. One can use only these roads to move from one city to another. There are no roads that connect a city to itself. For each pair of cities (*x*,<=*y*) there is at most one road from *x* to *y*.
A path from city *s* to city *t* is a sequence of cities *p*1, *p*2, ... , *p**k*, where *p*1<==<=*s*, *p**k*<==<=*t*, and there is a road from city *p**i* to city *p**i*<=+<=1 for each *i* from 1 to *k*<=-<=1. The path can pass multiple times through each city except *t*. It can't pass through *t* more than once.
A path *p* from *s* to *t* is ideal if it is the lexicographically minimal such path. In other words, *p* is ideal path from *s* to *t* if for any other path *q* from *s* to *t* *p**i*<=<<=*q**i*, where *i* is the minimum integer such that *p**i*<=≠<=*q**i*.
There is a tourist agency in the country that offers *q* unusual excursions: the *j*-th excursion starts at city *s**j* and ends in city *t**j*.
For each pair *s**j*, *t**j* help the agency to study the ideal path from *s**j* to *t**j*. Note that it is possible that there is no ideal path from *s**j* to *t**j*. This is possible due to two reasons:
- there is no path from *s**j* to *t**j*; - there are paths from *s**j* to *t**j*, but for every such path *p* there is another path *q* from *s**j* to *t**j*, such that *p**i*<=><=*q**i*, where *i* is the minimum integer for which *p**i*<=≠<=*q**i*.
The agency would like to know for the ideal path from *s**j* to *t**j* the *k**j*-th city in that path (on the way from *s**j* to *t**j*).
For each triple *s**j*, *t**j*, *k**j* (1<=≤<=*j*<=≤<=*q*) find if there is an ideal path from *s**j* to *t**j* and print the *k**j*-th city in that path, if there is any. | The first line contains three integers *n*, *m* and *q* (2<=≤<=*n*<=≤<=3000,0<=≤<=*m*<=≤<=3000, 1<=≤<=*q*<=≤<=4·105) — the number of cities, the number of roads and the number of excursions.
Each of the next *m* lines contains two integers *x**i* and *y**i* (1<=≤<=*x**i*,<=*y**i*<=≤<=*n*, *x**i*<=≠<=*y**i*), denoting that the *i*-th road goes from city *x**i* to city *y**i*. All roads are one-directional. There can't be more than one road in each direction between two cities.
Each of the next *q* lines contains three integers *s**j*, *t**j* and *k**j* (1<=≤<=*s**j*,<=*t**j*<=≤<=*n*, *s**j*<=≠<=*t**j*, 1<=≤<=*k**j*<=≤<=3000). | In the *j*-th line print the city that is the *k**j*-th in the ideal path from *s**j* to *t**j*. If there is no ideal path from *s**j* to *t**j*, or the integer *k**j* is greater than the length of this path, print the string '-1' (without quotes) in the *j*-th line. | [
"7 7 5\n1 2\n2 3\n1 3\n3 4\n4 5\n5 3\n4 6\n1 4 2\n2 6 1\n1 7 3\n1 3 2\n1 3 5\n"
] | [
"2\n-1\n-1\n2\n-1\n"
] | none | [
{
"input": "7 7 5\n1 2\n2 3\n1 3\n3 4\n4 5\n5 3\n4 6\n1 4 2\n2 6 1\n1 7 3\n1 3 2\n1 3 5",
"output": "2\n-1\n-1\n2\n-1"
},
{
"input": "3 4 5\n1 3\n2 1\n3 1\n3 2\n1 2 1\n2 3 2\n2 3 3\n1 3 1\n3 2 1",
"output": "-1\n1\n3\n1\n-1"
},
{
"input": "2 0 2\n2 1 2\n2 1 1",
"output": "-1\n-1"
},
{
"input": "4 0 1\n3 1 1",
"output": "-1"
},
{
"input": "2 1 3\n1 2\n1 2 1\n1 2 2\n1 2 1",
"output": "1\n2\n1"
},
{
"input": "2 1 5\n1 2\n1 2 1\n1 2 1\n1 2 1\n1 2 1\n1 2 1",
"output": "1\n1\n1\n1\n1"
},
{
"input": "2 0 1\n2 1 1",
"output": "-1"
},
{
"input": "5 7 10\n2 5\n3 5\n5 4\n5 2\n4 1\n1 4\n2 4\n4 2 3\n5 2 1\n1 3 3\n1 3 3\n3 2 2\n4 2 2\n3 5 3\n1 5 1\n3 5 1\n5 2 2",
"output": "-1\n5\n-1\n-1\n5\n-1\n-1\n-1\n3\n2"
},
{
"input": "10 11 10\n10 9\n5 10\n5 8\n2 5\n1 8\n3 4\n7 2\n4 6\n8 10\n6 7\n9 3\n3 2 1\n10 7 1\n7 5 2\n7 5 3\n10 5 2\n2 5 2\n10 4 2\n6 2 2\n6 2 1\n1 3 1",
"output": "3\n10\n2\n5\n9\n5\n9\n7\n6\n1"
},
{
"input": "10 15 10\n7 8\n1 4\n5 6\n10 9\n3 4\n10 3\n8 10\n1 2\n8 9\n10 1\n10 2\n4 5\n6 7\n2 3\n9 10\n2 1 3\n1 2 2\n2 3 1\n5 4 3\n3 5 2\n8 6 2\n2 7 1\n9 8 2\n1 9 2\n8 10 3",
"output": "4\n2\n2\n7\n4\n9\n2\n10\n2\n10"
},
{
"input": "10 16 20\n5 9\n6 3\n2 1\n9 2\n4 6\n5 10\n10 5\n6 8\n4 7\n4 8\n8 7\n7 4\n3 10\n9 10\n7 8\n1 2\n4 5 1\n9 1 1\n6 3 2\n6 3 2\n9 2 3\n3 2 6\n3 10 2\n6 10 3\n4 3 1\n6 10 3\n1 2 1\n4 3 3\n7 4 1\n7 1 7\n4 10 3\n5 9 2\n3 10 1\n3 1 1\n8 1 6\n6 10 3",
"output": "4\n9\n3\n3\n-1\n-1\n10\n10\n4\n10\n1\n3\n7\n9\n3\n9\n3\n3\n10\n10"
},
{
"input": "15 25 20\n9 7\n3 1\n7 3\n11 13\n1 6\n6 15\n12 13\n8 12\n4 11\n4 8\n3 5\n1 14\n3 12\n15 13\n5 2\n13 5\n15 10\n13 6\n13 9\n14 9\n2 14\n10 1\n13 10\n11 12\n2 12\n7 3 2\n10 8 2\n11 12 2\n4 8 1\n13 9 1\n6 8 1\n4 8 1\n9 8 1\n14 8 1\n11 1 2\n9 1 1\n7 6 1\n7 4 2\n11 2 1\n4 8 1\n12 5 1\n13 14 1\n9 3 1\n14 8 2\n7 10 2",
"output": "3\n-1\n12\n4\n-1\n-1\n4\n-1\n-1\n-1\n9\n7\n-1\n11\n4\n12\n-1\n9\n-1\n3"
},
{
"input": "20 20 40\n4 5\n6 7\n13 14\n10 11\n9 10\n19 20\n2 3\n1 2\n16 17\n8 9\n7 8\n15 16\n11 12\n5 6\n18 19\n17 18\n2 6\n14 15\n12 13\n3 4\n3 19 9\n3 18 13\n2 19 19\n2 18 12\n3 18 12\n1 18 8\n1 20 29\n3 19 12\n3 20 28\n1 19 27\n2 18 5\n2 18 28\n2 20 30\n1 20 26\n3 20 7\n1 20 23\n2 18 26\n3 18 21\n2 20 23\n1 20 23\n3 20 19\n2 18 27\n2 19 16\n2 18 10\n1 18 3\n3 18 25\n2 19 24\n3 18 21\n2 19 28\n2 20 23\n1 19 17\n2 19 28\n3 18 15\n3 19 29\n1 20 16\n2 19 22\n2 19 4\n1 20 22\n1 20 20\n2 19 13",
"output": "11\n15\n-1\n13\n14\n8\n-1\n14\n-1\n-1\n6\n-1\n-1\n-1\n9\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n17\n11\n3\n-1\n-1\n-1\n-1\n-1\n17\n-1\n17\n-1\n16\n-1\n5\n-1\n20\n14"
},
{
"input": "20 20 40\n3 4\n12 13\n2 3\n12 17\n4 5\n9 10\n11 12\n10 11\n12 15\n8 9\n5 6\n12 20\n12 16\n12 18\n1 2\n6 7\n15 11\n12 19\n12 14\n7 8\n3 9 19\n3 9 5\n2 9 22\n1 6 3\n2 9 22\n2 6 21\n3 6 21\n2 9 5\n1 4 29\n3 8 13\n2 5 19\n1 3 10\n1 3 4\n1 5 19\n2 6 24\n3 9 21\n2 3 9\n2 9 24\n2 3 30\n1 9 22\n2 8 28\n2 6 27\n1 3 17\n2 5 9\n3 2 30\n2 6 16\n1 6 21\n2 8 15\n3 5 23\n3 8 17\n1 5 12\n2 5 10\n3 9 4\n1 2 29\n1 2 26\n3 5 28\n2 4 28\n2 7 19\n3 8 5\n2 4 23",
"output": "-1\n7\n-1\n3\n-1\n-1\n-1\n6\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1\n6\n-1\n-1\n-1\n-1\n-1\n7\n-1"
}
] | 0 | 0 | -1 | 13,566 |
|
660 | Number of Parallelograms | [
"geometry"
] | null | null | You are given *n* points on a plane. All the points are distinct and no three of them lie on the same line. Find the number of parallelograms with the vertices at the given points. | The first line of the input contains integer *n* (1<=≤<=*n*<=≤<=2000) — the number of points.
Each of the next *n* lines contains two integers (*x**i*,<=*y**i*) (0<=≤<=*x**i*,<=*y**i*<=≤<=109) — the coordinates of the *i*-th point. | Print the only integer *c* — the number of parallelograms with the vertices at the given points. | [
"4\n0 1\n1 0\n1 1\n2 0\n"
] | [
"1\n"
] | none | [
{
"input": "4\n0 1\n1 0\n1 1\n2 0",
"output": "1"
},
{
"input": "1\n0 0",
"output": "0"
},
{
"input": "1\n6 6",
"output": "0"
},
{
"input": "5\n1 5\n4 2\n4 4\n8 1\n8 2",
"output": "0"
},
{
"input": "10\n1 7\n2 14\n3 7\n3 13\n5 13\n13 10\n15 12\n17 1\n18 8\n19 0",
"output": "2"
},
{
"input": "20\n0 17\n1 8\n1 9\n2 5\n2 11\n3 0\n5 10\n5 13\n6 7\n7 3\n12 13\n13 7\n14 16\n15 10\n15 18\n17 2\n17 12\n18 14\n19 18\n20 17",
"output": "18"
},
{
"input": "2\n2 5\n10 7",
"output": "0"
},
{
"input": "4\n7 9\n10 2\n12 20\n15 13",
"output": "1"
},
{
"input": "10\n2 14\n5 9\n10 16\n12 5\n16 19\n26 23\n30 37\n32 26\n37 33\n40 28",
"output": "10"
},
{
"input": "4\n0 0\n0 1\n1 2\n1 1",
"output": "1"
},
{
"input": "5\n4 0\n1 3\n0 3\n1 1\n4 2",
"output": "1"
},
{
"input": "4\n0 0\n1 0\n2 1\n1 1",
"output": "1"
},
{
"input": "8\n0 0\n0 2\n1 3\n1 1\n100 10\n100 11\n101 11\n101 10",
"output": "5"
},
{
"input": "4\n0 0\n0 1\n1000000000 0\n1000000000 1",
"output": "1"
},
{
"input": "4\n0 0\n0 1\n1 1\n1 0",
"output": "1"
},
{
"input": "8\n0 0\n1 1\n3 1\n2 0\n100 10\n100 11\n101 11\n101 10",
"output": "5"
},
{
"input": "4\n0 0\n1 1\n0 1\n1 0",
"output": "1"
},
{
"input": "4\n0 0\n0 2\n1 3\n1 1",
"output": "1"
},
{
"input": "6\n20 2\n20 3\n0 0\n0 1\n1 1\n1 0",
"output": "3"
},
{
"input": "4\n3 3\n4 4\n6 4\n5 3",
"output": "1"
},
{
"input": "4\n0 0\n1 1\n2 1\n1 0",
"output": "1"
},
{
"input": "5\n0 0\n1 1\n2 0\n1 4\n3 4",
"output": "1"
},
{
"input": "9\n6 4\n5 3\n1 4\n1 5\n5 0\n4 3\n4 0\n6 2\n2 1",
"output": "3"
},
{
"input": "4\n2 3\n2 1\n1 3\n1 1",
"output": "1"
},
{
"input": "4\n1 0\n2 0\n4 1\n3 1",
"output": "1"
},
{
"input": "4\n0 0\n1 1\n3 1\n2 0",
"output": "1"
},
{
"input": "4\n0 0\n1 1\n1 0\n0 1",
"output": "1"
},
{
"input": "4\n0 0\n1 0\n1000000000 1000000000\n999999999 1000000000",
"output": "1"
},
{
"input": "4\n1 0\n0 1000000000\n1 1\n2 2",
"output": "0"
},
{
"input": "4\n1 1\n2 1\n2 2\n1 2",
"output": "1"
},
{
"input": "4\n1 1\n2 2\n5 2\n4 1",
"output": "1"
},
{
"input": "4\n0 0\n0 1\n2 2\n2 1",
"output": "1"
},
{
"input": "4\n12 14\n15 19\n21 17\n18 12",
"output": "1"
},
{
"input": "4\n0 0\n0 1000000000\n1 0\n1 1000000000",
"output": "1"
},
{
"input": "4\n0 1\n1 0\n1 1\n0 2",
"output": "1"
},
{
"input": "6\n3 5\n3 15\n5 9\n5 19\n2 16\n4 20",
"output": "3"
},
{
"input": "4\n0 0\n2 2\n3 2\n1 0",
"output": "1"
},
{
"input": "6\n0 0\n0 4194304\n1 0\n1 2097152\n2 1\n2 8388609",
"output": "0"
}
] | 4,000 | 98,918,400 | 0 | 13,608 |
|
0 | none | [
"none"
] | null | null | Stepan is a very experienced olympiad participant. He has *n* cups for Physics olympiads and *m* cups for Informatics olympiads. Each cup is characterized by two parameters — its significance *c**i* and width *w**i*.
Stepan decided to expose some of his cups on a shelf with width *d* in such a way, that:
- there is at least one Physics cup and at least one Informatics cup on the shelf, - the total width of the exposed cups does not exceed *d*, - from each subjects (Physics and Informatics) some of the most significant cups are exposed (i. e. if a cup for some subject with significance *x* is exposed, then all the cups for this subject with significance greater than *x* must be exposed too).
Your task is to determine the maximum possible total significance, which Stepan can get when he exposes cups on the shelf with width *d*, considering all the rules described above. The total significance is the sum of significances of all the exposed cups. | The first line contains three integers *n*, *m* and *d* (1<=≤<=*n*,<=*m*<=≤<=100<=000, 1<=≤<=*d*<=≤<=109) — the number of cups for Physics olympiads, the number of cups for Informatics olympiads and the width of the shelf.
Each of the following *n* lines contains two integers *c**i* and *w**i* (1<=≤<=*c**i*,<=*w**i*<=≤<=109) — significance and width of the *i*-th cup for Physics olympiads.
Each of the following *m* lines contains two integers *c**j* and *w**j* (1<=≤<=*c**j*,<=*w**j*<=≤<=109) — significance and width of the *j*-th cup for Informatics olympiads. | Print the maximum possible total significance, which Stepan can get exposing cups on the shelf with width *d*, considering all the rules described in the statement.
If there is no way to expose cups on the shelf, then print 0. | [
"3 1 8\n4 2\n5 5\n4 2\n3 2\n",
"4 3 12\n3 4\n2 4\n3 5\n3 4\n3 5\n5 2\n3 4\n",
"2 2 2\n5 3\n6 3\n4 2\n8 1\n"
] | [
"8\n",
"11\n",
"0\n"
] | In the first example Stepan has only one Informatics cup which must be exposed on the shelf. Its significance equals 3 and width equals 2, so after Stepan exposes it, the width of free space on the shelf becomes equal to 6. Also, Stepan must expose the second Physics cup (which has width 5), because it is the most significant cup for Physics (its significance equals 5). After that Stepan can not expose more cups on the shelf, because there is no enough free space. Thus, the maximum total significance of exposed cups equals to 8. | [
{
"input": "3 1 8\n4 2\n5 5\n4 2\n3 2",
"output": "8"
},
{
"input": "4 3 12\n3 4\n2 4\n3 5\n3 4\n3 5\n5 2\n3 4",
"output": "11"
},
{
"input": "2 2 2\n5 3\n6 3\n4 2\n8 1",
"output": "0"
},
{
"input": "10 10 229\n15 17\n5 4\n4 15\n4 17\n15 11\n7 6\n5 19\n14 8\n4 1\n10 12\n20 13\n20 14\n16 13\n7 15\n2 16\n11 11\n19 20\n6 7\n4 11\n14 16",
"output": "198"
},
{
"input": "10 20 498\n40 12\n23 25\n20 9\n8 1\n23 8\n31 24\n33 2\n22 33\n4 13\n25 20\n40 5\n27 5\n17 6\n8 5\n4 19\n33 23\n30 19\n27 12\n13 22\n16 32\n28 36\n20 18\n36 38\n9 24\n21 35\n20 9\n33 29\n29 33\n18 25\n11 8",
"output": "644"
},
{
"input": "20 10 761\n42 41\n47 7\n35 6\n22 40\n15 2\n47 28\n46 47\n3 45\n12 19\n44 41\n46 2\n49 23\n9 8\n7 41\n5 3\n16 42\n12 50\n17 22\n25 9\n45 12\n41 44\n34 47\n33 35\n32 47\n49 6\n27 18\n43 36\n23 6\n39 22\n38 45",
"output": "900"
},
{
"input": "1 1 1000000000\n4 500000000\n6 500000000",
"output": "10"
},
{
"input": "4 2 8\n1000000000 2\n1000000000 2\n1000000000 2\n1000000000 2\n1000000000 2\n1000000000 2",
"output": "4000000000"
},
{
"input": "1 1 1000000000\n1 1000000000\n1 1000000000",
"output": "0"
},
{
"input": "1 1 1\n1 1\n1 1",
"output": "0"
}
] | 1,949 | 23,756,800 | 0 | 13,665 |
|
321 | Ciel and Robot | [
"binary search",
"implementation",
"math"
] | null | null | Fox Ciel has a robot on a 2D plane. Initially it is located in (0, 0). Fox Ciel code a command to it. The command was represented by string *s*. Each character of *s* is one move operation. There are four move operations at all:
- 'U': go up, (x, y) <=→<= (x, y+1); - 'D': go down, (x, y) <=→<= (x, y-1); - 'L': go left, (x, y) <=→<= (x-1, y); - 'R': go right, (x, y) <=→<= (x+1, y).
The robot will do the operations in *s* from left to right, and repeat it infinite times. Help Fox Ciel to determine if after some steps the robot will located in (*a*,<=*b*). | The first line contains two integers *a* and *b*, (<=-<=109<=≤<=*a*,<=*b*<=≤<=109). The second line contains a string *s* (1<=≤<=|*s*|<=≤<=100, *s* only contains characters 'U', 'D', 'L', 'R') — the command. | Print "Yes" if the robot will be located at (*a*,<=*b*), and "No" otherwise. | [
"2 2\nRU\n",
"1 2\nRU\n",
"-1 1000000000\nLRRLU\n",
"0 0\nD\n"
] | [
"Yes\n",
"No\n",
"Yes\n",
"Yes\n"
] | In the first and second test case, command string is "RU", so the robot will go right, then go up, then right, and then up and so on.
The locations of its moves are (0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → ...
So it can reach (2, 2) but not (1, 2). | [
{
"input": "2 2\nRU",
"output": "Yes"
},
{
"input": "1 2\nRU",
"output": "No"
},
{
"input": "-1 1000000000\nLRRLU",
"output": "Yes"
},
{
"input": "0 0\nD",
"output": "Yes"
},
{
"input": "0 0\nUURRDL",
"output": "Yes"
},
{
"input": "987654321 987654321\nUURRDL",
"output": "Yes"
},
{
"input": "4 2\nUURRDL",
"output": "No"
},
{
"input": "4 3\nUURRDL",
"output": "Yes"
},
{
"input": "4 4\nUURRDL",
"output": "Yes"
},
{
"input": "4 6\nUURRDL",
"output": "Yes"
},
{
"input": "4 7\nUURRDL",
"output": "No"
},
{
"input": "1000000000 1000000000\nUURRDL",
"output": "Yes"
},
{
"input": "-1 -1\nUR",
"output": "No"
},
{
"input": "1 1\nUURRDDLL",
"output": "No"
},
{
"input": "987654321 2\nUURDD",
"output": "Yes"
},
{
"input": "0 123456789\nRRULL",
"output": "Yes"
},
{
"input": "4 4\nUUUURRRRDDDDLLLL",
"output": "Yes"
},
{
"input": "-491226083 -49122610\nUDRLDURLDLLLDUDURLRDUUDDUUULUDRDRDUULURDRLLDDDLUDUURLUUDLLDULLLLDDLDDUU",
"output": "Yes"
},
{
"input": "-261597957 418556728\nLLLDLUDUULLRDDULLRRUDRDLULRLRLLRRUUDRRLRUDLRRLUDRDLLUUDUULRURLDLULUUULDDUURLRUDURRL",
"output": "Yes"
},
{
"input": "-771928144 -3\nRUDULULDRDLLLULDDUDDDDUDULRULRUULDDDURUDLUURULLLDLLDDRDDRLRURUULRUURRUDLDLDDRLLULRRDRRLLUULUDRUUDRRD",
"output": "Yes"
},
{
"input": "397346346 1\nDDURRUURLDLRRLULD",
"output": "Yes"
},
{
"input": "-528551525 0\nUDRLRRLDLDLURRRRULDLRLRLURUUDDLRLLDRRULLUDLURDLUUULLLRUUUDRRURLDUDULDDRDDDRDL",
"output": "Yes"
},
{
"input": "311692421 -129871846\nLLLDURULDDDDUDDURRLUUDRLDDRDURDDRUDUURLUDUDLDRUDDDUUURDRRUDRDRDURLLDURUUDRLDLDURRRRRRDULURDRU",
"output": "Yes"
},
{
"input": "485940814 728911221\nURURU",
"output": "Yes"
},
{
"input": "-843450986 632588242\nLURLULULRUDUDULRDDLUL",
"output": "Yes"
},
{
"input": "647999516 -809999401\nUDLDDLLULUDDLLDUULRRRDLUDDLDDLRLRRDRURURDRRDRULUDRDULRULLRRLLDDRLRRUDRURDUULUDLRRLRDR",
"output": "Yes"
},
{
"input": "352820537 -764444491\nRDDUDLUDDUDLRRRDRRRDRRDUDUDDURLRRLDRLLRLLLLUULUDRURRDRLDDLLDRDURDUDRUDDLUDRLURUDRURDRDDLDRLDLDLLU",
"output": "Yes"
},
{
"input": "-284973644 -1\nDLULLDLRUUDRR",
"output": "Yes"
},
{
"input": "356922591 -2\nRRLDLDUDRUUUULUUDDULDDUDD",
"output": "No"
},
{
"input": "27033101 54066203\nUDDDRDLLLRUUDDLRDLDRLRUDDULRLLRULR",
"output": "No"
},
{
"input": "-199335150 39867031\nLLURRDUULRUDDRDUUULDLDRDDLURDRLDRLLLRRRRRULRRRUUDD",
"output": "No"
},
{
"input": "609504072 609504074\nULRLUDLDDR",
"output": "No"
},
{
"input": "497684357 829473929\nRRLDUUURULURRLLRRLRLURRLDU",
"output": "Yes"
},
{
"input": "551922835 183974295\nDUDUUULDRLRURRDULRRUDDLRLLUULLRLRDRDRR",
"output": "No"
},
{
"input": "825368095 -825368096\nRD",
"output": "No"
},
{
"input": "-458990423 -229495204\nDLLDDRLUDLRLUL",
"output": "No"
},
{
"input": "285102789 570205594\nRRDULRULULRRDUURRLURUDDULLRDUL",
"output": "No"
},
{
"input": "109928480 219856920\nLRURLRLURDRDLDRDLRDDUUDDLULDRRUUURRUDLLUULUUUR",
"output": "No"
},
{
"input": "-532674020 532674026\nUURLLL",
"output": "No"
},
{
"input": "999999999 0\nRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR",
"output": "Yes"
},
{
"input": "0 0\nUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLR",
"output": "Yes"
},
{
"input": "1 1\nUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLRUDLR",
"output": "No"
},
{
"input": "-1000000000 -1000000000\nDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDLDL",
"output": "Yes"
},
{
"input": "3 3\nUURR",
"output": "No"
},
{
"input": "-2 -2\nUR",
"output": "No"
},
{
"input": "5 5\nUDLR",
"output": "No"
},
{
"input": "0 -1\nU",
"output": "No"
},
{
"input": "-1 0\nR",
"output": "No"
},
{
"input": "1000000000 1000000000\nURURURUR",
"output": "Yes"
},
{
"input": "-1 -1\nRU",
"output": "No"
},
{
"input": "1 1\nLD",
"output": "No"
},
{
"input": "-2 -2\nUURR",
"output": "No"
},
{
"input": "1000000000 0\nRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR",
"output": "Yes"
},
{
"input": "2 6\nRUUUURLDDDL",
"output": "Yes"
},
{
"input": "0 1\nLUUR",
"output": "No"
},
{
"input": "1 1\nURDLDL",
"output": "Yes"
},
{
"input": "-10 -10\nRU",
"output": "No"
},
{
"input": "1000000000 1000000000\nRURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURURU",
"output": "Yes"
},
{
"input": "-1000000000 -500000000\nURR",
"output": "No"
},
{
"input": "-2 0\nULLLDDRRRR",
"output": "Yes"
},
{
"input": "999999999 -999999999\nRRRRRRRRRRRRRRRRRRRRRRRRRDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLLLUUUUUUUUUUUUUUUUUUUUUUU",
"output": "Yes"
},
{
"input": "-100 -100\nRU",
"output": "No"
},
{
"input": "100 100\nRUL",
"output": "No"
},
{
"input": "0 1\nUDLR",
"output": "Yes"
},
{
"input": "0 1\nD",
"output": "No"
},
{
"input": "0 -3\nRDDL",
"output": "No"
}
] | 248 | 0 | 0 | 13,693 |
|
91 | Queue | [
"binary search",
"data structures"
] | B. Queue | 2 | 256 | There are *n* walruses standing in a queue in an airport. They are numbered starting from the queue's tail: the 1-st walrus stands at the end of the queue and the *n*-th walrus stands at the beginning of the queue. The *i*-th walrus has the age equal to *a**i*.
The *i*-th walrus becomes displeased if there's a younger walrus standing in front of him, that is, if exists such *j* (*i*<=<<=*j*), that *a**i*<=><=*a**j*. The displeasure of the *i*-th walrus is equal to the number of walruses between him and the furthest walrus ahead of him, which is younger than the *i*-th one. That is, the further that young walrus stands from him, the stronger the displeasure is.
The airport manager asked you to count for each of *n* walruses in the queue his displeasure. | The first line contains an integer *n* (2<=≤<=*n*<=≤<=105) — the number of walruses in the queue. The second line contains integers *a**i* (1<=≤<=*a**i*<=≤<=109).
Note that some walruses can have the same age but for the displeasure to emerge the walrus that is closer to the head of the queue needs to be strictly younger than the other one. | Print *n* numbers: if the *i*-th walrus is pleased with everything, print "-1" (without the quotes). Otherwise, print the *i*-th walrus's displeasure: the number of other walruses that stand between him and the furthest from him younger walrus. | [
"6\n10 8 5 3 50 45\n",
"7\n10 4 6 3 2 8 15\n",
"5\n10 3 1 10 11\n"
] | [
"2 1 0 -1 0 -1 ",
"4 2 1 0 -1 -1 -1 ",
"1 0 -1 -1 -1 "
] | none | [
{
"input": "6\n10 8 5 3 50 45",
"output": "2 1 0 -1 0 -1 "
},
{
"input": "7\n10 4 6 3 2 8 15",
"output": "4 2 1 0 -1 -1 -1 "
},
{
"input": "5\n10 3 1 10 11",
"output": "1 0 -1 -1 -1 "
},
{
"input": "13\n18 9 8 9 23 20 18 18 33 25 31 37 36",
"output": "2 0 -1 -1 2 1 -1 -1 1 -1 -1 0 -1 "
},
{
"input": "10\n15 21 17 22 27 21 31 26 32 30",
"output": "-1 0 -1 1 2 -1 2 -1 0 -1 "
},
{
"input": "10\n18 20 18 17 17 13 22 20 34 29",
"output": "4 3 2 1 0 -1 0 -1 0 -1 "
},
{
"input": "13\n16 14 12 9 11 28 30 21 35 30 32 31 43",
"output": "3 2 1 -1 -1 1 0 -1 2 -1 0 -1 -1 "
},
{
"input": "15\n18 6 18 21 14 20 13 9 18 20 28 13 19 25 21",
"output": "10 -1 8 8 6 6 0 -1 2 2 3 -1 -1 0 -1 "
},
{
"input": "11\n15 17 18 18 26 22 23 33 33 21 29",
"output": "-1 -1 -1 -1 4 3 2 2 1 -1 -1 "
},
{
"input": "15\n14 4 5 12 6 19 14 19 12 22 23 17 14 21 27",
"output": "7 -1 -1 0 -1 6 1 4 -1 3 2 0 -1 -1 -1 "
},
{
"input": "2\n1 1000000000",
"output": "-1 -1 "
},
{
"input": "2\n1000000000 1",
"output": "0 -1 "
},
{
"input": "5\n15 1 8 15 3",
"output": "3 -1 1 0 -1 "
},
{
"input": "12\n5 1 2 5 100 1 1000 100 10000 20000 10000 20000",
"output": "4 -1 2 1 0 -1 0 -1 -1 0 -1 -1 "
}
] | 748 | 12,288,000 | 3.790112 | 13,700 |
55 | Beautiful numbers | [
"dp",
"number theory"
] | D. Beautiful numbers | 4 | 256 | Volodya is an odd boy and his taste is strange as well. It seems to him that a positive integer number is beautiful if and only if it is divisible by each of its nonzero digits. We will not argue with this and just count the quantity of beautiful numbers in given ranges. | The first line of the input contains the number of cases *t* (1<=≤<=*t*<=≤<=10). Each of the next *t* lines contains two natural numbers *l**i* and *r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=9<=·1018).
Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d). | Output should contain *t* numbers — answers to the queries, one number per line — quantities of beautiful numbers in given intervals (from *l**i* to *r**i*, inclusively). | [
"1\n1 9\n",
"1\n12 15\n"
] | [
"9\n",
"2\n"
] | none | [
{
"input": "1\n1 9",
"output": "9"
},
{
"input": "1\n12 15",
"output": "2"
},
{
"input": "1\n25 53",
"output": "7"
},
{
"input": "1\n1 1000",
"output": "138"
},
{
"input": "1\n1 100000",
"output": "4578"
},
{
"input": "2\n234 59843\n46 3243",
"output": "3378\n381"
},
{
"input": "4\n55 55\n1234 2348\n620 620\n4 1000",
"output": "1\n135\n0\n135"
},
{
"input": "1\n1 9000000000000000000",
"output": "15957349671845566"
},
{
"input": "5\n5397562498 1230483490253448\n39218765 5293867493184739\n99 999999999999\n546234 2394748365397856\n67 801834",
"output": "3974776165902\n15977172601197\n5429986145\n7654830993719\n26117"
},
{
"input": "3\n1 1\n9000000000000000000 9000000000000000000\n8999999999999999999 8999999999999999999",
"output": "1\n1\n0"
},
{
"input": "9\n357816591093473912 478906145736655650\n154072099530098530 297675544560923083\n853274171983555776 877332810632329118\n258601077826366175 856890041027686262\n151084241340128367 868279055062218946\n360302714872207562 400114081267420149\n15181634044326791 602401427137909762\n85295343866069509 372373854804747278\n61825864286248332 820583114541565140",
"output": "262303539156695\n312897266661597\n38778726789519\n1139862940345127\n1402615778591617\n79118901111096\n1245376292216844\n659738283968181\n1512151848646298"
},
{
"input": "7\n104609317611013150 341289880328203892\n97241912027543222 314418300699926877\n53441135299739439 389735416311904624\n275391517859532788 467960038909170238\n304318532879803217 768089672739846481\n319824835697587963 736305171087865698\n409387390360731466 545771099640557323",
"output": "549953639217759\n500330757015166\n752572674468163\n436944574287103\n888035593458099\n815512909354668\n274130616468780"
},
{
"input": "9\n445541835776354804 558734188486271358\n73682036065176542 366947184576839560\n308564620247881013 586289290590337947\n191966067909858814 427579642915908767\n96549472115040860 524715559221512354\n255020036710938147 654502276995773879\n80176357776022017 657344223781591909\n16719475415528318 443326279724654990\n338052544981592129 686095491515876947",
"output": "201308654973933\n671018900952294\n557260640825456\n540245067535034\n951590675251248\n821822247331406\n1236063703297355\n975752055142342\n695221153195519"
},
{
"input": "8\n423727899203401096 465066089007515233\n592099166919122847 693326943315408193\n231531173552972562 531446476635170028\n716633579315369700 812280907158531602\n418627020920440527 499027876613131004\n163898261665251882 822784355862669948\n435839418352342371 467127616759016838\n485096651053655121 650414421921269042",
"output": "95861671721858\n223094952917814\n644166606425537\n120467904177516\n171364758258616\n1283490622790032\n70087190765465\n307069761298908"
},
{
"input": "10\n317170715064111090 793355628628194180\n739156054415396992 777408930205278114\n190203742284298612 871433095584843953\n299464632866349604 887366147454183925\n604292320992752545 686849525965889579\n671343144075216807 887426356575285220\n29419076620738966 587651333431204877\n623639325649517323 649463206025796889\n433988870372201677 826343090001917979\n59211672688034983 185391377687885100",
"output": "882906430841196\n42022148935039\n1331583561781769\n1112192163424357\n187737287429964\n340983354590699\n1187362489423650\n65177281203879\n681151115425128\n281120105826732"
},
{
"input": "10\n284628591358250298 646259693733499061\n124314877444536921 158360653417589331\n294802485707819594 348409229744008981\n600000720865727637 612539571868349067\n43148541126130378 706710122330555006\n623654284391810432 864058024613618266\n96275043624390708 878551347136533260\n101314040620664356 877345387577542422\n330459790968153544 396766608075635018\n437750508922390426 606265056174456186",
"output": "747510034316095\n79156178606166\n135124732730027\n34085557037263\n1399630254414422\n411736949395029\n1554771181008711\n1542736445406160\n140533045281525\n291140888308231"
},
{
"input": "2\n699477065952458657 872009205627849715\n125384274193311446 322714849067940236",
"output": "264558248920386\n447564169675211"
},
{
"input": "5\n287022480899155515 575607276198133575\n269577246853440756 493029962385944199\n33867048981266469 753806197266881614\n122720683292361468 585860767594869710\n158415500607290576 291208960498755656",
"output": "592269002835278\n490392318097910\n1479332749456685\n973971824970712\n293817273058831"
},
{
"input": "7\n256594007991864539 522344824090301945\n244974983299956912 369564779245483014\n389003124143900342 870218470015550418\n195460950995683388 651270783906429493\n346224221518880818 866785151789106062\n253038155332981304 335508507616974071\n90600597989420506 233249608331610512",
"output": "569988591376813\n279165427586805\n878614839734539\n963922382771989\n955701376330903\n185737826200532\n335147883567859"
},
{
"input": "4\n1316690822130409 43473794526140271\n31324963681870844 400596320533679208\n145052817797209833 830063350205257021\n158658407621553147 888417552777282422",
"output": "111729862958642\n828223557472883\n1338195829521665\n1422989272142417"
},
{
"input": "5\n54466217578737820 199602944107455170\n590840692238108171 845011715230237399\n13556617965656361 472040489988635161\n714035286668109810 850408020486632812\n300350088832329391 447391742372023290",
"output": "315665808201383\n452173335782140\n1043520592810950\n207881845406015\n346723658222085"
},
{
"input": "5\n319233236657111501 439203315902660433\n576536153378125966 581498392015228293\n211896470192814609 802604291686025035\n276426676181343125 621591075446200211\n508640487982063778 534483221559283380",
"output": "275614372867493\n4659637264553\n1137342068923219\n699280378176787\n43498698267824"
},
{
"input": "2\n109665811875257879 257740418232519221\n604210587139443191 625314575765100157",
"output": "346819987743014\n55092823341467"
},
{
"input": "6\n268178188710040742 576988663070502189\n504550929759464987 781375970672533626\n383664952430952316 634627265571145187\n32079280703703870 854176930200007145\n91332009005179043 184053275183946180\n40615673830587752 81118443341384874",
"output": "626997097457560\n461119872685266\n494669041669140\n1651825364810407\n212939340175502\n81771949489938"
},
{
"input": "6\n302303335070090868 450003809972976938\n38797475097975886 362745244153909054\n255979212134580442 584044352113226014\n296314585958572870 577227175635398364\n62422561943575682 256080854477707325\n211472647017729730 238012961902478501",
"output": "346244647306943\n735804706209393\n662539475305881\n575163541821522\n442982474060829\n69445242386875"
},
{
"input": "2\n682002069204224661 741697951489458142\n183681502765856661 640437699585130293",
"output": "88198304176240\n962081125874149"
},
{
"input": "10\n139335835151468925 484066860116557425\n263442856552254877 313125870358044935\n251857673095776569 867489314560690117\n537516700522410653 723282616279678271\n395380521908450082 806672097008414136\n235871329996145263 884796582724269557\n534443148879117170 654182410587394685\n380572226198783846 879140470933346585\n44215071468435238 258286912303970378\n26312939052691831 729014058195540988",
"output": "768880516070086\n105251422042778\n1171842666779485\n340594731814913\n733127744647337\n1237953582953797\n227668828811669\n906919615037865\n483212415948596\n1471096234030452"
},
{
"input": "1\n409932656755767888 555182693984224688",
"output": "288403268897055"
},
{
"input": "5\n85486498031991129 609519488362467658\n580104402950188545 585551649929612890\n266889485749089795 290577696596475568\n29875185901092149 120388080236728441\n287513302314456963 523308494771522710",
"output": "1105188916073505\n8401535899653\n42676144797046\n203278778614845\n511366630991705"
},
{
"input": "5\n19182336056148152 208792307948641418\n679752014854666194 698235312605408252\n171120031998422805 569721388031168451\n12148793149507654 583293559019372679\n132953494234881925 342019770688732055",
"output": "428539359425062\n38145118408539\n843379203441666\n1226321445918381\n477944627277795"
},
{
"input": "1\n290788238061324166 326414205793715944",
"output": "88194728799125"
},
{
"input": "5\n234980802136837794 678684394174931737\n379107007207217021 898625960325636363\n299786954727403405 471077420542543174\n128226582798019699 763298680395163050\n211161692546607273 384187742288440244",
"output": "912901045635585\n946264344323228\n396530582015099\n1276195957822587\n393055025121430"
},
{
"input": "5\n89021901785536018 721970357006512096\n10455209854982 672121404159230388\n177585137659819353 575574850046871820\n65145962073623720 680133228947272669\n391876042757036995 669425246021613653",
"output": "1326519621640374\n1455095002395873\n839815657146984\n1301765297380635\n556427727905125"
},
{
"input": "7\n759792714318263446 835705573208322900\n460742320949633715 470758694665495415\n415505837605910991 569430654167207205\n377168676014875291 658290859272415183\n283793404702060566 304952201274598832\n511204209665235974 673646757429123938\n204114397228198672 797985176265960222",
"output": "125479708961158\n23959650169069\n295105797092887\n558580533111335\n46911931274954\n306769834874325\n1148348273935072"
},
{
"input": "9\n84911486803129062 371360395960886607\n215284546951446780 821388426823792006\n166750422723367513 332960369043386392\n656713493264874130 830533243210221453\n279192318807285719 846434989742407222\n184571653844680221 502821438236701008\n158613676606887401 202707248716070578\n57540730334410124 60880782285483617\n180003597833276637 824443392811852241",
"output": "659040707264401\n1169272353137522\n376194188156988\n265702711225992\n1082952205541968\n710617267557674\n90657680784523\n5900863115303\n1261270219463080"
},
{
"input": "8\n57710938094283125 133772303709577393\n225971608986591641 527160269434785752\n326606700768403490 501974015736773213\n104238980296659530 597665360857507536\n129585992859086273 782985334217822917\n95949900165719335 509445717207521416\n282373530338110359 395331940454914825\n109101574779985403 119360877564462401",
"output": "174229855050036\n652036071424638\n380051677908779\n1036346035129658\n1296518899055801\n926646671294788\n253442916135262\n27096176893815"
},
{
"input": "6\n143809081082381724 710709485503956307\n477002227475791129 748415761498654762\n194250190495612708 722691609433551584\n75162568328377570 286478648363940215\n167009103400266860 565869134050802277\n502744098916587217 886107958887143606",
"output": "1174608615264406\n478873948513061\n1088489184647499\n477237176264941\n845730891804138\n655620551892311"
},
{
"input": "7\n44244599058777278 782140424182656491\n253187103338885776 695335736560569599\n29699011635943174 255027033171638318\n620123105021375390 632580504164439237\n15375925200954959 514151645969327190\n543405682133478575 609214152593311339\n319215262961370608 516830493012444317",
"output": "1483854651250762\n905015525981812\n517553165213234\n33709204034254\n1113374351058951\n100352641671765\n426472119432887"
},
{
"input": "9\n126345625290218706 784850219000022089\n87023426041824251 129119697169349357\n115069371829617205 505544318183729913\n101524249349082603 410056021854163969\n365868821220246374 407398810119575711\n430453801123321243 449066562720974247\n343735112634641611 864077546788537811\n40949324306296116 718988450894528392\n374523541044751782 624503429430134549",
"output": "1305739310768597\n102116549043209\n871997518159200\n702650020836287\n83143533290706\n47299584944773\n955940809894257\n1421553310960175\n483847068411766"
},
{
"input": "6\n628054167404305809 628631960105352883\n76614448048985164 664591413517666821\n262907302737145633 436561742851767924\n546542973469933497 609783019570052293\n144878328150224178 587802477340215629\n418802873287839235 492960279487924481",
"output": "1567925255004\n1257931500816068\n392229959274848\n95900315764706\n917682338726377\n160732132866347"
},
{
"input": "4\n314756235091775713 527675415702104393\n262211905544992553 474539845101486132\n650849880923001511 686127592579746738\n302723886566715571 800643954239584448",
"output": "453938626100478\n474023849716525\n67782962321158\n928258453065819"
},
{
"input": "10\n459047565386426124 557194352219781174\n334174633100816445 574518777618872908\n339256617206207374 461702378236276473\n588718051366049429 591583237944573629\n279503563837328065 787989497738844701\n21523491428669060 804432015267107086\n176599362925115382 372462231016537122\n86537781617987114 189304598553178698\n752344156097144261 806368993421691027\n823292318017906645 846671299523066080",
"output": "175044419962203\n475567289515459\n271613608429105\n3445772208321\n966370135430115\n1572574434602937\n449309541759218\n233323955652174\n64992990053986\n52429533514265"
},
{
"input": "8\n235988693924367721 871763392821283031\n831354122145544757 897628959367475233\n208456624263360265 304233837602695736\n564455930754426325 747724855342153655\n733111142906877033 788390309965048178\n105753118324937331 227328301612681221\n89981956803108752 608240082487490427\n247970213583436454 274499034399377923",
"output": "1217007726638431\n122388636057875\n217887979666251\n326178731297371\n61066928664641\n284737008145535\n1093373317372355\n53748508684990"
},
{
"input": "3\n106944629644846234 868784028501976520\n609893146415774201 829549590949963820\n280831004762390139 860314575937399777",
"output": "1516745018492261\n379777276962608\n1101541359723373"
},
{
"input": "6\n43993555587390686 472396927744198873\n166115563323012274 740944002931589125\n745385119308013664 778824408151010477\n298307917637500505 739076799736050705\n270559504032562580 324248373286245715\n445587297201428883 453886541051311950",
"output": "964419689750151\n1163718720277976\n36086421106555\n874162586490607\n118661992679784\n16505740933228"
},
{
"input": "7\n617593704688843596 828119736217232389\n3293204449283890 690109219324558805\n175366679625274382 211592984052182604\n134013605241468389 156621244614592310\n87651424533962276 294531661482220423\n652576309304110648 855895695568516689\n477666266196006205 647707658685159920",
"output": "355371372539710\n1476637881473656\n78566652210064\n51957130064357\n470606070577295\n325555975457004\n316743540058033"
},
{
"input": "10\n50041481631208215 447762572637187951\n168215116153505310 514436306319509511\n247862097199125155 712191937735295742\n98125769392212035 345332927057490352\n351553192787723038 775772738657478138\n412742092029203073 627638533260248401\n196268314021034051 765318785061421414\n129127817256091656 848467628311779115\n209408331444736026 477286893553657979\n199077079465747558 382720611537297379",
"output": "901252368499013\n758846043617857\n939353740423384\n579394703095088\n778021740563806\n409454897225469\n1132337130752633\n1422718774146674\n606275219995081\n421492007921185"
},
{
"input": "9\n360616474860484616 383999497202599749\n309747278163068128 324627518197345788\n37810933547908346 442701859960681398\n206321505581033547 517952468011059058\n830707273735965413 838545144291501943\n481064567699374119 637860173392597272\n64724838137416918 401453198057895626\n90969763647055934 161655002682127994\n832701350006309129 863335897035281262",
"output": "46498133371402\n40850597316229\n919493060637341\n687618814419970\n17501208925553\n286355733364676\n752235164806132\n170035203610447\n60213403274850"
},
{
"input": "2\n17998572321587853 467288454221606647\n123156820907183052 834785732165266684",
"output": "1024878648284905\n1407846459864944"
},
{
"input": "1\n1 999999999999999999",
"output": "1986512740492024"
},
{
"input": "1\n191919191919191919 919191919191919191",
"output": "1412002458948136"
},
{
"input": "10\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919\n7090909090909090909 8191919191919191919",
"output": "1308643426185330\n1308643426185330\n1308643426185330\n1308643426185330\n1308643426185330\n1308643426185330\n1308643426185330\n1308643426185330\n1308643426185330\n1308643426185330"
},
{
"input": "10\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555\n5555555555555555555 5555555555555555555",
"output": "1\n1\n1\n1\n1\n1\n1\n1\n1\n1"
},
{
"input": "6\n312118719 8999999999291228845\n667149650 8999999999517267203\n913094187 8999999999725405253\n154899869 8999999999515635472\n17006149 8999999999611234564\n557783437 8999999999450461526",
"output": "15957349664614135\n15957349661485914\n15957349660288369\n15957349667743907\n15957349670077199\n15957349662484120"
},
{
"input": "3\n49395813 8999999999232681026\n130560985 8999999999732049698\n561847056 8999999999660238105",
"output": "15957349668110658\n15957349668753664\n15957349663087863"
},
{
"input": "5\n988020422 8999999999820367297\n146385894 8999999999144649284\n647276749 8999999999118469703\n545904849 8999999999653000715\n66157176 8999999999517239977",
"output": "15957349659989376\n15957349666269127\n15957349660004094\n15957349663205409\n15957349669084965"
},
{
"input": "4\n159528081 8999999999254686152\n155140195 8999999999221118378\n573463040 8999999999924740913\n984536526 8999999999076714216",
"output": "15957349666612744\n15957349666487217\n15957349663881451\n15957349657279299"
},
{
"input": "10\n79746525 8999999999623095709\n107133428 8999999999011808285\n395554969 8999999999078624899\n617453363 8999999999094258969\n152728928 8999999999672481523\n252006040 8999999999766225306\n547017602 8999999999444173567\n765495515 8999999999421300177\n974820465 8999999999294163554\n560970841 8999999999720023934",
"output": "15957349669242168\n15957349666397845\n15957349662613062\n15957349660358569\n15957349668236046\n15957349666959085\n15957349662552352\n15957349660553361\n15957349658288950\n15957349663286963"
},
{
"input": "8\n989660313 8999999999396148104\n74305000 8999999999742113337\n122356523 8999999999305515797\n592472806 8999999999132041329\n241537546 8999999999521843612\n885836059 8999999999480097833\n636266002 8999999999732372739\n202992959 8999999999981938988",
"output": "15957349658680891\n15957349669642622\n15957349667387215\n15957349660885350\n15957349666468387\n15957349659758751\n15957349662500550\n15957349668676585"
},
{
"input": "6\n367798644 8999999999638151319\n332338496 8999999999040457114\n623242741 8999999999949105799\n531142995 8999999999535909314\n717090981 8999999999596647230\n158402883 8999999999599697481",
"output": "15957349665093234\n15957349663187787\n15957349663490125\n15957349662956630\n15957349661257647\n15957349667853562"
},
{
"input": "5\n956765583 8999999999016337994\n370504871 8999999999584832832\n419407328 8999999999309673477\n518267114 8999999999030078889\n575673403 8999999999079982623",
"output": "15957349657174545\n15957349664842554\n15957349663287444\n15957349660934012\n15957349660687410"
},
{
"input": "3\n739134224 8999999999892539778\n960410270 8999999999024682694\n286103376 8999999999849390015",
"output": "15957349662121656\n15957349657206147\n15957349666880631"
},
{
"input": "4\n674378376 8999999999719931608\n37509017 8999999999387372213\n406034921 8999999999018438724\n546125539 8999999999879368044",
"output": "15957349662041057\n15957349668957044\n15957349662212605\n15957349663840013"
},
{
"input": "4\n840893847 8999999999654562383\n139840441 8999999999921619811\n311512855 8999999999801704512\n25959825 8999999999551930487",
"output": "15957349660688006\n15957349669232504\n15957349666299121\n15957349669765189"
},
{
"input": "7\n89870013 8999999999917755425\n802311555 8999999999055366008\n847333505 8999999999726653552\n132149035 8999999999144498325\n943135535 8999999999038849200\n820468253 8999999999630582637\n369473186 8999999999168524327",
"output": "15957349670087446\n15957349658761550\n15957349660810956\n15957349666520206\n15957349657360988\n15957349660817284\n15957349663250037"
},
{
"input": "5\n508307251 8999999999718177123\n521516981 8999999999464659141\n290241176 8999999999356325428\n615193857 8999999999597603944\n207549445 8999999999906844873",
"output": "15957349663733007\n15957349662832928\n15957349665236045\n15957349662359742\n15957349668276315"
},
{
"input": "2\n27550482 8999999999973770612\n120156054 8999999999028557489",
"output": "15957349671150714\n15957349666232530"
},
{
"input": "1\n271055852 8999999999909378243",
"output": "15957349667254063"
},
{
"input": "8\n787842267 8999999999359738007\n133322301 8999999999943290774\n417668696 8999999999749402497\n46587622 8999999999589402579\n718959740 8999999999109688815\n529442028 8999999999809940983\n943175645 8999999999567139418\n865545527 8999999999260702769",
"output": "15957349660173586\n15957349669437416\n15957349664824777\n15957349669455115\n15957349659354335\n15957349663684224\n15957349659508226\n15957349658965833"
},
{
"input": "10\n1883143 8999999999664400380\n373522758 8999999999528614034\n49945668 8999999999257821295\n659209563 8999999999455232186\n74336065 8999999999709871509\n97315679 8999999999108629997\n112069256 8999999999626576439\n12161303 8999999999432219862\n756831002 8999999999681371635\n230283719 8999999999550291145",
"output": "15957349670641976\n15957349664736116\n15957349668207957\n15957349661419878\n15957349669602216\n15957349667015648\n15957349668768809\n15957349669676588\n15957349661437380\n15957349666718051"
}
] | 60 | 0 | 0 | 13,717 |
0 | none | [
"none"
] | null | null | Карта звёздного неба представляет собой прямоугольное поле, состоящее из *n* строк по *m* символов в каждой строке. Каждый символ — это либо «.» (означает пустой участок неба), либо «*» (означает то, что в этом месте на небе есть звезда).
Новое издание карты звёздного неба будет напечатано на квадратных листах, поэтому требуется найти минимально возможную сторону квадрата, в который могут поместиться все звезды. Границы искомого квадрата должны быть параллельны сторонам заданного прямоугольного поля. | В первой строке входных данных записаны два числа *n* и *m* (1<=≤<=*n*,<=*m*<=≤<=1000) — количество строк и столбцов на карте звездного неба.
В следующих *n* строках задано по *m* символов. Каждый символ — это либо «.» (пустой участок неба), либо «*» (звезда).
Гарантируется, что на небе есть хотя бы одна звезда. | Выведите одно число — минимально возможную сторону квадрата, которым можно накрыть все звезды. | [
"4 4\n....\n..*.\n...*\n..**\n",
"1 3\n*.*\n",
"2 1\n.\n*\n"
] | [
"3\n",
"3\n",
"1\n"
] | Один из возможных ответов на первый тестовый пример:
Один из возможных ответов на второй тестовый пример (обратите внимание, что покрывающий квадрат выходит за пределы карты звездного неба):
Ответ на третий тестовый пример: | [
{
"input": "4 4\n....\n..*.\n...*\n..**",
"output": "3"
},
{
"input": "1 3\n*.*",
"output": "3"
},
{
"input": "2 1\n.\n*",
"output": "1"
},
{
"input": "1 1\n*",
"output": "1"
},
{
"input": "1 2\n.*",
"output": "1"
},
{
"input": "1 2\n*.",
"output": "1"
},
{
"input": "1 2\n**",
"output": "2"
},
{
"input": "2 1\n.\n*",
"output": "1"
},
{
"input": "2 1\n*\n.",
"output": "1"
},
{
"input": "2 1\n*\n*",
"output": "2"
},
{
"input": "5 3\n..*\n.**\n..*\n...\n..*",
"output": "5"
},
{
"input": "1 1\n*",
"output": "1"
},
{
"input": "1 2\n*.",
"output": "1"
},
{
"input": "1 2\n**",
"output": "2"
},
{
"input": "1 3\n.**",
"output": "2"
},
{
"input": "1 3\n*.*",
"output": "3"
},
{
"input": "1 4\n..**",
"output": "2"
},
{
"input": "1 4\n*..*",
"output": "4"
},
{
"input": "1 5\n.*.**",
"output": "4"
},
{
"input": "1 5\n.*..*",
"output": "4"
},
{
"input": "2 1\n*\n.",
"output": "1"
},
{
"input": "2 1\n*\n*",
"output": "2"
},
{
"input": "2 2\n.*\n..",
"output": "1"
},
{
"input": "2 2\n*.\n.*",
"output": "2"
},
{
"input": "2 3\n*..\n**.",
"output": "2"
},
{
"input": "2 3\n*..\n..*",
"output": "3"
},
{
"input": "2 4\n.***\n.*.*",
"output": "3"
},
{
"input": "2 5\n*..**\n.*.*.",
"output": "5"
},
{
"input": "2 5\n.....\n*.*..",
"output": "3"
},
{
"input": "3 1\n*\n*\n*",
"output": "3"
},
{
"input": "3 1\n*\n.\n*",
"output": "3"
},
{
"input": "3 2\n..\n..\n**",
"output": "2"
},
{
"input": "3 2\n.*\n.*\n..",
"output": "2"
},
{
"input": "3 3\n*..\n.**\n***",
"output": "3"
},
{
"input": "3 4\n..*.\n....\n..*.",
"output": "3"
},
{
"input": "3 5\n.....\n.*...\n..*..",
"output": "2"
},
{
"input": "4 1\n.\n.\n*\n*",
"output": "2"
},
{
"input": "4 1\n*\n.\n*\n.",
"output": "3"
},
{
"input": "4 2\n*.\n*.\n.*\n**",
"output": "4"
},
{
"input": "4 2\n*.\n..\n..\n.*",
"output": "4"
},
{
"input": "4 3\n..*\n...\n...\n*..",
"output": "4"
},
{
"input": "4 4\n..*.\n..*.\n.*..\n***.",
"output": "4"
},
{
"input": "4 4\n....\n...*\n....\n..*.",
"output": "3"
},
{
"input": "5 1\n*\n*\n.\n.\n.",
"output": "2"
},
{
"input": "5 1\n*\n.\n.\n.\n*",
"output": "5"
},
{
"input": "5 2\n.*\n**\n**\n..\n**",
"output": "5"
},
{
"input": "5 2\n*.\n..\n..\n..\n.*",
"output": "5"
},
{
"input": "5 3\n...\n***\n..*\n.**\n**.",
"output": "4"
},
{
"input": "5 3\n*..\n...\n...\n...\n.*.",
"output": "5"
},
{
"input": "5 4\n*.**\n.*..\n.*..\n..*.\n*..*",
"output": "5"
},
{
"input": "5 4\n....\n..*.\n....\n....\n..*.",
"output": "4"
},
{
"input": "5 5\n....*\n....*\n....*\n..*..\n..*.*",
"output": "5"
},
{
"input": "2 2\n**\n**",
"output": "2"
},
{
"input": "2 2\n*.\n.*",
"output": "2"
},
{
"input": "2 2\n.*\n*.",
"output": "2"
},
{
"input": "2 2\n**\n..",
"output": "2"
},
{
"input": "2 2\n..\n**",
"output": "2"
},
{
"input": "2 2\n*.\n*.",
"output": "2"
},
{
"input": "2 2\n.*\n.*",
"output": "2"
},
{
"input": "2 2\n*.\n..",
"output": "1"
},
{
"input": "2 2\n.*\n..",
"output": "1"
},
{
"input": "2 2\n..\n*.",
"output": "1"
},
{
"input": "2 2\n..\n.*",
"output": "1"
},
{
"input": "2 2\n.*\n**",
"output": "2"
},
{
"input": "2 2\n*.\n**",
"output": "2"
},
{
"input": "2 2\n**\n.*",
"output": "2"
},
{
"input": "2 2\n**\n*.",
"output": "2"
}
] | 77 | 6,144,000 | 3 | 13,724 |
|
777 | Hanoi Factory | [
"brute force",
"data structures",
"dp",
"greedy",
"sortings"
] | null | null | Of course you have heard the famous task about Hanoi Towers, but did you know that there is a special factory producing the rings for this wonderful game? Once upon a time, the ruler of the ancient Egypt ordered the workers of Hanoi Factory to create as high tower as possible. They were not ready to serve such a strange order so they had to create this new tower using already produced rings.
There are *n* rings in factory's stock. The *i*-th ring has inner radius *a**i*, outer radius *b**i* and height *h**i*. The goal is to select some subset of rings and arrange them such that the following conditions are satisfied:
- Outer radiuses form a non-increasing sequence, i.e. one can put the *j*-th ring on the *i*-th ring only if *b**j*<=≤<=*b**i*. - Rings should not fall one into the the other. That means one can place ring *j* on the ring *i* only if *b**j*<=><=*a**i*. - The total height of all rings used should be maximum possible. | The first line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=100<=000) — the number of rings in factory's stock.
The *i*-th of the next *n* lines contains three integers *a**i*, *b**i* and *h**i* (1<=≤<=*a**i*,<=*b**i*,<=*h**i*<=≤<=109, *b**i*<=><=*a**i*) — inner radius, outer radius and the height of the *i*-th ring respectively. | Print one integer — the maximum height of the tower that can be obtained. | [
"3\n1 5 1\n2 6 2\n3 7 3\n",
"4\n1 2 1\n1 3 3\n4 6 2\n5 7 1\n"
] | [
"6\n",
"4\n"
] | In the first sample, the optimal solution is to take all the rings and put them on each other in order 3, 2, 1.
In the second sample, one can put the ring 3 on the ring 4 and get the tower of height 3, or put the ring 1 on the ring 2 and get the tower of height 4. | [
{
"input": "3\n1 5 1\n2 6 2\n3 7 3",
"output": "6"
},
{
"input": "4\n1 2 1\n1 3 3\n4 6 2\n5 7 1",
"output": "4"
},
{
"input": "1\n1 2 1",
"output": "1"
},
{
"input": "5\n6 10 4\n9 20 19\n8 11 18\n18 20 1\n19 20 8",
"output": "50"
},
{
"input": "5\n21 25 26\n14 30 22\n6 29 30\n13 23 21\n10 11 5",
"output": "99"
},
{
"input": "5\n45 73 26\n59 73 29\n30 74 9\n59 63 72\n73 84 79",
"output": "215"
},
{
"input": "9\n1 5 1000000000\n23 27 834000000\n6 10 1000000000\n26 30 234500000\n5 9 1000000000\n2 6 1000000000\n3 7 1000000000\n24 29 132400000\n25 28 23400000",
"output": "5000000000"
},
{
"input": "10\n312 838 197\n713 996 320\n427 767 520\n490 800 465\n575 681 995\n781 843 908\n545 615 400\n36 667 129\n85 641 27\n396 539 350",
"output": "3961"
},
{
"input": "15\n3 14 531\n28 29 17\n7 10 512\n20 21 264\n8 9 52\n16 19 759\n1 30 391\n2 27 861\n17 18 357\n15 22 428\n24 25 588\n23 26 221\n6 13 413\n11 12 667\n4 5 513",
"output": "2863"
},
{
"input": "15\n7 8 940377876\n5 26 602265950\n18 19 193066910\n23 24 754826087\n2 3 555140266\n6 25 830980693\n27 28 636793242\n20 21 809913904\n1 30 868457738\n10 17 698644057\n9 22 443624155\n13 16 941205435\n14 15 42481040\n4 29 305295425\n11 12 765921496",
"output": "4732954493"
},
{
"input": "15\n10 11 552706512\n24 25 708893662\n18 19 731182554\n12 13 110677554\n28 29 938846280\n1 30 898802132\n16 17 89748120\n2 3 85944653\n6 7 141693677\n14 15 432017874\n4 5 498032180\n22 23 906122257\n8 9 561584264\n20 21 98373932\n26 27 195705303",
"output": "1837648412"
},
{
"input": "15\n1 30 902215054\n12 13 463027806\n9 14 846985104\n20 21 770345346\n17 22 514758030\n2 15 438137019\n18 19 278467923\n16 29 613043570\n10 11 765879041\n6 7 960155075\n26 27 323764310\n24 25 724736351\n4 5 107208241\n3 8 992951987\n23 28 70277204",
"output": "3293459135"
},
{
"input": "3\n1 3 1\n4 5 1\n2 5 1",
"output": "3"
},
{
"input": "5\n1 3 1000000000\n4 5 1000000000\n2 5 1000000000\n4 6 1000000000\n5 6 1000000000",
"output": "5000000000"
}
] | 62 | 0 | 0 | 13,730 |
|
731 | 80-th Level Archeology | [
"brute force",
"data structures",
"greedy",
"sortings"
] | null | null | Archeologists have found a secret pass in the dungeon of one of the pyramids of Cycleland. To enter the treasury they have to open an unusual lock on the door. The lock consists of *n* words, each consisting of some hieroglyphs. The wall near the lock has a round switch. Each rotation of this switch changes the hieroglyphs according to some rules. The instruction nearby says that the door will open only if words written on the lock would be sorted in lexicographical order (the definition of lexicographical comparison in given in notes section).
The rule that changes hieroglyphs is the following. One clockwise rotation of the round switch replaces each hieroglyph with the next hieroglyph in alphabet, i.e. hieroglyph *x* (1<=≤<=*x*<=≤<=*c*<=-<=1) is replaced with hieroglyph (*x*<=+<=1), and hieroglyph *c* is replaced with hieroglyph 1.
Help archeologist determine, how many clockwise rotations they should perform in order to open the door, or determine that this is impossible, i.e. no cyclic shift of the alphabet will make the sequence of words sorted lexicographically. | The first line of the input contains two integers *n* and *c* (2<=≤<=*n*<=≤<=500<=000, 1<=≤<=*c*<=≤<=106) — the number of words, written on the lock, and the number of different hieroglyphs.
Each of the following *n* lines contains the description of one word. The *i*-th of these lines starts with integer *l**i* (1<=≤<=*l**i*<=≤<=500<=000), that denotes the length of the *i*-th word, followed by *l**i* integers *w**i*,<=1, *w**i*,<=2, ..., *w**i*,<=*l**i* (1<=≤<=*w**i*,<=*j*<=≤<=*c*) — the indices of hieroglyphs that make up the *i*-th word. Hieroglyph with index 1 is the smallest in the alphabet and with index *c* — the biggest.
It's guaranteed, that the total length of all words doesn't exceed 106. | If it is possible to open the door by rotating the round switch, print integer *x* (0<=≤<=*x*<=≤<=*c*<=-<=1) that defines the required number of clockwise rotations. If there are several valid *x*, print any of them.
If it is impossible to open the door by this method, print <=-<=1. | [
"4 3\n2 3 2\n1 1\n3 2 3 1\n4 2 3 1 2\n",
"2 5\n2 4 2\n2 4 2\n",
"4 4\n1 2\n1 3\n1 4\n1 2\n"
] | [
"1\n",
"0\n",
"-1\n"
] | Word *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*m*</sub> of length *m* is lexicographically not greater than word *b*<sub class="lower-index">1</sub>, *b*<sub class="lower-index">2</sub>, ..., *b*<sub class="lower-index">*k*</sub> of length *k*, if one of two conditions hold:
- at first position *i*, such that *a*<sub class="lower-index">*i*</sub> ≠ *b*<sub class="lower-index">*i*</sub>, the character *a*<sub class="lower-index">*i*</sub> goes earlier in the alphabet than character *b*<sub class="lower-index">*i*</sub>, i.e. *a* has smaller character in the first position where they differ; - if there is no such position *i* and *m* ≤ *k*, i.e. the first word is a prefix of the second or two words are equal.
The sequence of words is said to be sorted in lexicographical order if each word (except the last one) is lexicographically not greater than the next word.
In the first sample, after the round switch is rotated 1 position clockwise the words look as follows:
In the second sample, words are already sorted in lexicographical order.
In the last sample, one can check that no shift of the alphabet will work. | [
{
"input": "4 3\n2 3 2\n1 1\n3 2 3 1\n4 2 3 1 2",
"output": "1"
},
{
"input": "2 5\n2 4 2\n2 4 2",
"output": "0"
},
{
"input": "4 4\n1 2\n1 3\n1 4\n1 2",
"output": "-1"
},
{
"input": "3 1\n2 1 1\n2 1 1\n3 1 1 1",
"output": "0"
},
{
"input": "2 10\n14 9 6 7 1 6 9 3 1 9 4 6 8 8 1\n3 3 7 6",
"output": "2"
},
{
"input": "5 10\n1 5\n7 5 1 10 5 3 7 10\n1 2\n1 3\n7 4 7 3 9 4 6 1",
"output": "6"
},
{
"input": "50 5\n1 4\n1 4\n1 4\n1 4\n2 4 4\n2 4 5\n2 4 5\n3 4 1 1\n4 4 1 2 5\n7 4 3 2 1 4 4 5\n1 5\n1 5\n1 5\n1 5\n2 5 4\n2 5 5\n2 5 5\n2 5 1\n2 5 3\n1 1\n1 1\n1 1\n1 1\n2 1 4\n2 1 4\n2 1 5\n2 1 1\n2 1 1\n2 1 3\n9 1 3 4 3 2 5 5 5 2\n1 2\n1 2\n3 2 4 2\n2 2 1\n2 2 2\n2 2 2\n2 2 2\n1 3\n1 2\n1 3\n1 3\n1 3\n1 3\n1 3\n2 3 4\n3 3 4 4\n5 3 4 5 2 1\n2 3 5\n2 3 2\n2 3 3",
"output": "-1"
},
{
"input": "10 10\n2 6 6\n1 7\n1 8\n2 8 2\n2 9 2\n2 10 5\n1 1\n1 4\n3 4 9 3\n2 5 1",
"output": "5"
}
] | 77 | 0 | 0 | 13,805 |
|
439 | Devu and his Brother | [
"binary search",
"sortings",
"ternary search",
"two pointers"
] | null | null | Devu and his brother love each other a lot. As they are super geeks, they only like to play with arrays. They are given two arrays *a* and *b* by their father. The array *a* is given to Devu and *b* to his brother.
As Devu is really a naughty kid, he wants the minimum value of his array *a* should be at least as much as the maximum value of his brother's array *b*.
Now you have to help Devu in achieving this condition. You can perform multiple operations on the arrays. In a single operation, you are allowed to decrease or increase any element of any of the arrays by 1. Note that you are allowed to apply the operation on any index of the array multiple times.
You need to find minimum number of operations required to satisfy Devu's condition so that the brothers can play peacefully without fighting. | The first line contains two space-separated integers *n*, *m* (1<=≤<=*n*,<=*m*<=≤<=105). The second line will contain *n* space-separated integers representing content of the array *a* (1<=≤<=*a**i*<=≤<=109). The third line will contain *m* space-separated integers representing content of the array *b* (1<=≤<=*b**i*<=≤<=109). | You need to output a single integer representing the minimum number of operations needed to satisfy Devu's condition. | [
"2 2\n2 3\n3 5\n",
"3 2\n1 2 3\n3 4\n",
"3 2\n4 5 6\n1 2\n"
] | [
"3\n",
"4\n",
"0\n"
] | In example 1, you can increase *a*<sub class="lower-index">1</sub> by 1 and decrease *b*<sub class="lower-index">2</sub> by 1 and then again decrease *b*<sub class="lower-index">2</sub> by 1. Now array *a* will be [3; 3] and array *b* will also be [3; 3]. Here minimum element of *a* is at least as large as maximum element of *b*. So minimum number of operations needed to satisfy Devu's condition are 3.
In example 3, you don't need to do any operation, Devu's condition is already satisfied. | [
{
"input": "2 2\n2 3\n3 5",
"output": "3"
},
{
"input": "3 2\n1 2 3\n3 4",
"output": "4"
},
{
"input": "3 2\n4 5 6\n1 2",
"output": "0"
},
{
"input": "10 10\n23 100 38 38 73 54 59 69 44 86\n100 100 100 100 100 100 100 100 100 100",
"output": "416"
},
{
"input": "1 1\n401114\n998223974",
"output": "997822860"
},
{
"input": "1 1\n100\n4",
"output": "0"
},
{
"input": "1 1\n100\n183299",
"output": "183199"
},
{
"input": "1 1\n999999999\n1000000000",
"output": "1"
},
{
"input": "1 1\n1000000000\n1000000000",
"output": "0"
},
{
"input": "1 1\n1\n2",
"output": "1"
},
{
"input": "1 1\n1\n1",
"output": "0"
},
{
"input": "1 1\n2\n1",
"output": "0"
},
{
"input": "1 1\n1\n2",
"output": "1"
},
{
"input": "1 1\n1\n3",
"output": "2"
},
{
"input": "1 2\n1\n2 2",
"output": "1"
},
{
"input": "2 1\n2 2\n3",
"output": "1"
}
] | 140 | 20,172,800 | 0 | 13,814 |
|
977 | Cyclic Components | [
"dfs and similar",
"dsu",
"graphs"
] | null | null | You are given an undirected graph consisting of $n$ vertices and $m$ edges. Your task is to find the number of connected components which are cycles.
Here are some definitions of graph theory.
An undirected graph consists of two sets: set of nodes (called vertices) and set of edges. Each edge connects a pair of vertices. All edges are bidirectional (i.e. if a vertex $a$ is connected with a vertex $b$, a vertex $b$ is also connected with a vertex $a$). An edge can't connect vertex with itself, there is at most one edge between a pair of vertices.
Two vertices $u$ and $v$ belong to the same connected component if and only if there is at least one path along edges connecting $u$ and $v$.
A connected component is a cycle if and only if its vertices can be reordered in such a way that:
- the first vertex is connected with the second vertex by an edge, - the second vertex is connected with the third vertex by an edge, - ... - the last vertex is connected with the first vertex by an edge, - all the described edges of a cycle are distinct.
A cycle doesn't contain any other edges except described above. By definition any cycle contains three or more vertices. | The first line contains two integer numbers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5$, $0 \le m \le 2 \cdot 10^5$) — number of vertices and edges.
The following $m$ lines contains edges: edge $i$ is given as a pair of vertices $v_i$, $u_i$ ($1 \le v_i, u_i \le n$, $u_i \ne v_i$). There is no multiple edges in the given graph, i.e. for each pair ($v_i, u_i$) there no other pairs ($v_i, u_i$) and ($u_i, v_i$) in the list of edges. | Print one integer — the number of connected components which are also cycles. | [
"5 4\n1 2\n3 4\n5 4\n3 5\n",
"17 15\n1 8\n1 12\n5 11\n11 9\n9 15\n15 5\n4 13\n3 13\n4 3\n10 16\n7 10\n16 7\n14 3\n14 4\n17 6\n"
] | [
"1\n",
"2\n"
] | In the first example only component $[3, 4, 5]$ is also a cycle.
The illustration above corresponds to the second example. | [
{
"input": "5 4\n1 2\n3 4\n5 4\n3 5",
"output": "1"
},
{
"input": "17 15\n1 8\n1 12\n5 11\n11 9\n9 15\n15 5\n4 13\n3 13\n4 3\n10 16\n7 10\n16 7\n14 3\n14 4\n17 6",
"output": "2"
},
{
"input": "4 4\n1 2\n2 3\n1 3\n1 4",
"output": "0"
},
{
"input": "5 5\n1 2\n2 3\n3 4\n4 1\n3 5",
"output": "0"
},
{
"input": "200000 0",
"output": "0"
},
{
"input": "1 0",
"output": "0"
},
{
"input": "5 10\n1 2\n2 3\n3 4\n4 5\n5 1\n1 4\n2 4\n3 5\n3 1\n2 5",
"output": "0"
},
{
"input": "5 10\n1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 4\n3 5\n4 5",
"output": "0"
},
{
"input": "6 9\n1 2\n2 3\n3 4\n4 5\n5 6\n6 1\n6 2\n2 4\n6 4",
"output": "0"
},
{
"input": "4 6\n1 2\n2 3\n3 4\n4 1\n1 3\n2 4",
"output": "0"
}
] | 1,887 | 99,840,000 | 3 | 13,815 |
|
869 | The Intriguing Obsession | [
"combinatorics",
"dp",
"math"
] | null | null | — This is not playing but duty as allies of justice, Nii-chan!
— Not allies but justice itself, Onii-chan!
With hands joined, go everywhere at a speed faster than our thoughts! This time, the Fire Sisters — Karen and Tsukihi — is heading for somewhere they've never reached — water-surrounded islands!
There are three clusters of islands, conveniently coloured red, blue and purple. The clusters consist of *a*, *b* and *c* distinct islands respectively.
Bridges have been built between some (possibly all or none) of the islands. A bridge bidirectionally connects two different islands and has length 1. For any two islands of the same colour, either they shouldn't be reached from each other through bridges, or the shortest distance between them is at least 3, apparently in order to prevent oddities from spreading quickly inside a cluster.
The Fire Sisters are ready for the unknown, but they'd also like to test your courage. And you're here to figure out the number of different ways to build all bridges under the constraints, and give the answer modulo 998<=244<=353. Two ways are considered different if a pair of islands exist, such that there's a bridge between them in one of them, but not in the other. | The first and only line of input contains three space-separated integers *a*, *b* and *c* (1<=≤<=*a*,<=*b*,<=*c*<=≤<=5<=000) — the number of islands in the red, blue and purple clusters, respectively. | Output one line containing an integer — the number of different ways to build bridges, modulo 998<=244<=353. | [
"1 1 1\n",
"1 2 2\n",
"1 3 5\n",
"6 2 9\n"
] | [
"8\n",
"63\n",
"3264\n",
"813023575\n"
] | In the first example, there are 3 bridges that can possibly be built, and no setup of bridges violates the restrictions. Thus the answer is 2<sup class="upper-index">3</sup> = 8.
In the second example, the upper two structures in the figure below are instances of valid ones, while the lower two are invalid due to the blue and purple clusters, respectively. | [
{
"input": "1 1 1",
"output": "8"
},
{
"input": "1 2 2",
"output": "63"
},
{
"input": "1 3 5",
"output": "3264"
},
{
"input": "6 2 9",
"output": "813023575"
},
{
"input": "7 3 7",
"output": "807577560"
},
{
"input": "135 14 39",
"output": "414849507"
},
{
"input": "5000 5000 5000",
"output": "986778560"
},
{
"input": "2 1 1",
"output": "18"
},
{
"input": "1 1 3",
"output": "32"
},
{
"input": "1 2 3",
"output": "156"
},
{
"input": "4 1 2",
"output": "315"
},
{
"input": "5 9 4",
"output": "661093467"
},
{
"input": "4 2 5",
"output": "326151"
},
{
"input": "9 4 10",
"output": "391175867"
},
{
"input": "16 8 29",
"output": "349763770"
},
{
"input": "17 46 45",
"output": "518654435"
},
{
"input": "28 47 1",
"output": "517406193"
},
{
"input": "94 87 10",
"output": "846321893"
},
{
"input": "84 29 61",
"output": "391253501"
},
{
"input": "179 856 377",
"output": "518957210"
},
{
"input": "1925 1009 273",
"output": "207866159"
},
{
"input": "1171 2989 2853",
"output": "234725427"
},
{
"input": "3238 2923 4661",
"output": "636587126"
},
{
"input": "1158 506 4676",
"output": "6109065"
},
{
"input": "4539 2805 2702",
"output": "356944655"
},
{
"input": "4756 775 3187",
"output": "56242066"
},
{
"input": "4998 4998 4998",
"output": "259368717"
},
{
"input": "4996 1 5000",
"output": "196902859"
},
{
"input": "2048 4096 1024",
"output": "445542375"
},
{
"input": "5000 1 1",
"output": "50020002"
}
] | 171 | 1,536,000 | 0 | 13,834 |
|
303 | Lucky Permutation Triple | [
"constructive algorithms",
"implementation",
"math"
] | null | null | Bike is interested in permutations. A permutation of length *n* is an integer sequence such that each integer from 0 to (*n*<=-<=1) appears exactly once in it. For example, [0,<=2,<=1] is a permutation of length 3 while both [0,<=2,<=2] and [1,<=2,<=3] is not.
A permutation triple of permutations of length *n* (*a*,<=*b*,<=*c*) is called a Lucky Permutation Triple if and only if . The sign *a**i* denotes the *i*-th element of permutation *a*. The modular equality described above denotes that the remainders after dividing *a**i*<=+<=*b**i* by *n* and dividing *c**i* by *n* are equal.
Now, he has an integer *n* and wants to find a Lucky Permutation Triple. Could you please help him? | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=105). | If no Lucky Permutation Triple of length *n* exists print -1.
Otherwise, you need to print three lines. Each line contains *n* space-seperated integers. The first line must contain permutation *a*, the second line — permutation *b*, the third — permutation *c*.
If there are multiple solutions, print any of them. | [
"5\n",
"2\n"
] | [
"1 4 3 2 0\n1 0 2 4 3\n2 4 0 1 3\n",
"-1\n"
] | In Sample 1, the permutation triple ([1, 4, 3, 2, 0], [1, 0, 2, 4, 3], [2, 4, 0, 1, 3]) is Lucky Permutation Triple, as following holds:
- <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/a6bf1b9b57809dbec5021f65f89616f259587c07.png" style="max-width: 100.0%;max-height: 100.0%;"/>; - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/48cc13134296b68f459f69d78e0240859aaec702.png" style="max-width: 100.0%;max-height: 100.0%;"/>; - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ac44412de7b46833e90348a6b3298f9796e3977c.png" style="max-width: 100.0%;max-height: 100.0%;"/>; - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3825b0bb758208dda2ead1c5224c05d89ad9ab55.png" style="max-width: 100.0%;max-height: 100.0%;"/>; - <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0a72e2da40048a507839927a211267ac01c9bf89.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
In Sample 2, you can easily notice that no lucky permutation triple exists. | [
{
"input": "5",
"output": "1 4 3 2 0\n1 0 2 4 3\n2 4 0 1 3"
},
{
"input": "2",
"output": "-1"
},
{
"input": "8",
"output": "-1"
},
{
"input": "9",
"output": "0 1 2 3 4 5 6 7 8 \n0 1 2 3 4 5 6 7 8 \n0 2 4 6 8 1 3 5 7 "
},
{
"input": "2",
"output": "-1"
},
{
"input": "77",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 \n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 \n0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 4..."
},
{
"input": "6",
"output": "-1"
},
{
"input": "87",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 \n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 \n0 2 4..."
},
{
"input": "72",
"output": "-1"
},
{
"input": "1",
"output": "0 \n0 \n0 "
},
{
"input": "23",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 \n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 \n0 2 4 6 8 10 12 14 16 18 20 22 1 3 5 7 9 11 13 15 17 19 21 "
},
{
"input": "52",
"output": "-1"
},
{
"input": "32",
"output": "-1"
},
{
"input": "25",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 \n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 \n0 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 "
},
{
"input": "54",
"output": "-1"
},
{
"input": "39",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 \n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 \n0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 "
},
{
"input": "20",
"output": "-1"
},
{
"input": "53",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 \n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 \n0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 "
},
{
"input": "34",
"output": "-1"
},
{
"input": "23",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 \n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 \n0 2 4 6 8 10 12 14 16 18 20 22 1 3 5 7 9 11 13 15 17 19 21 "
},
{
"input": "37123",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 1..."
},
{
"input": "41904",
"output": "-1"
},
{
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},
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},
{
"input": "1",
"output": "0 \n0 \n0 "
},
{
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"output": "-1"
},
{
"input": "99999",
"output": "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 1..."
},
{
"input": "99998",
"output": "-1"
}
] | 748 | 10,240,000 | 3 | 13,879 |
|
583 | Robot's Task | [
"greedy",
"implementation"
] | null | null | Robot Doc is located in the hall, with *n* computers stand in a line, numbered from left to right from 1 to *n*. Each computer contains exactly one piece of information, each of which Doc wants to get eventually. The computers are equipped with a security system, so to crack the *i*-th of them, the robot needs to collect at least *a**i* any pieces of information from the other computers. Doc can hack the computer only if he is right next to it.
The robot is assembled using modern technologies and can move along the line of computers in either of the two possible directions, but the change of direction requires a large amount of resources from Doc. Tell the minimum number of changes of direction, which the robot will have to make to collect all *n* parts of information if initially it is next to computer with number 1.
It is guaranteed that there exists at least one sequence of the robot's actions, which leads to the collection of all information. Initially Doc doesn't have any pieces of information. | The first line contains number *n* (1<=≤<=*n*<=≤<=1000). The second line contains *n* non-negative integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=<<=*n*), separated by a space. It is guaranteed that there exists a way for robot to collect all pieces of the information. | Print a single number — the minimum number of changes in direction that the robot will have to make in order to collect all *n* parts of information. | [
"3\n0 2 0\n",
"5\n4 2 3 0 1\n",
"7\n0 3 1 0 5 2 6\n"
] | [
"1\n",
"3\n",
"2\n"
] | In the first sample you can assemble all the pieces of information in the optimal manner by assembling first the piece of information in the first computer, then in the third one, then change direction and move to the second one, and then, having 2 pieces of information, collect the last piece.
In the second sample to collect all the pieces of information in the optimal manner, Doc can go to the fourth computer and get the piece of information, then go to the fifth computer with one piece and get another one, then go to the second computer in the same manner, then to the third one and finally, to the first one. Changes of direction will take place before moving from the fifth to the second computer, then from the second to the third computer, then from the third to the first computer.
In the third sample the optimal order of collecting parts from computers can look like that: 1->3->4->6->2->5->7. | [
{
"input": "3\n0 2 0",
"output": "1"
},
{
"input": "5\n4 2 3 0 1",
"output": "3"
},
{
"input": "7\n0 3 1 0 5 2 6",
"output": "2"
},
{
"input": "1\n0",
"output": "0"
},
{
"input": "2\n0 1",
"output": "0"
},
{
"input": "10\n0 0 0 0 0 0 0 0 0 0",
"output": "0"
},
{
"input": "3\n0 2 1",
"output": "1"
},
{
"input": "10\n7 1 9 3 5 8 6 0 2 4",
"output": "9"
},
{
"input": "10\n1 3 5 7 9 8 6 4 2 0",
"output": "9"
},
{
"input": "10\n5 0 0 1 3 2 2 2 5 7",
"output": "1"
},
{
"input": "10\n8 6 5 3 9 7 1 4 2 0",
"output": "8"
},
{
"input": "10\n1 2 4 5 0 1 3 7 1 4",
"output": "2"
},
{
"input": "10\n3 4 8 9 5 1 2 0 6 7",
"output": "6"
},
{
"input": "10\n2 2 0 0 6 2 9 0 2 0",
"output": "2"
},
{
"input": "10\n1 7 5 3 2 6 0 8 4 9",
"output": "8"
},
{
"input": "9\n1 3 8 6 2 4 5 0 7",
"output": "7"
},
{
"input": "9\n1 3 5 7 8 6 4 2 0",
"output": "8"
},
{
"input": "9\n2 4 3 1 3 0 5 4 3",
"output": "3"
},
{
"input": "9\n3 5 6 8 7 0 4 2 1",
"output": "5"
},
{
"input": "9\n2 0 8 1 0 3 0 5 3",
"output": "2"
},
{
"input": "9\n6 2 3 7 4 8 5 1 0",
"output": "4"
},
{
"input": "9\n3 1 5 6 0 3 2 0 0",
"output": "2"
},
{
"input": "9\n2 6 4 1 0 8 5 3 7",
"output": "7"
},
{
"input": "100\n27 20 18 78 93 38 56 2 48 75 36 88 96 57 69 10 25 74 68 86 65 85 66 14 22 12 43 80 99 34 42 63 61 71 77 15 37 54 21 59 23 94 28 30 50 84 62 76 47 16 26 64 82 92 72 53 17 11 41 91 35 83 79 95 67 13 1 7 3 4 73 90 8 19 33 58 98 32 39 45 87 52 60 46 6 44 49 70 51 9 5 29 31 24 40 97 81 0 89 55",
"output": "69"
},
{
"input": "100\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70 68 66 64 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0",
"output": "99"
},
{
"input": "100\n13 89 81 0 62 1 59 92 29 13 1 37 2 8 53 15 20 34 12 70 0 85 97 55 84 60 37 54 14 65 22 69 30 22 95 44 59 85 50 80 9 71 91 93 74 21 11 78 28 21 40 81 76 24 26 60 48 85 61 68 89 76 46 73 34 52 98 29 4 38 94 51 5 55 6 27 74 27 38 37 82 70 44 89 51 59 30 37 15 55 63 78 42 39 71 43 4 10 2 13",
"output": "21"
},
{
"input": "100\n1 3 5 7 58 11 13 15 17 19 45 23 25 27 29 31 33 35 37 39 41 43 21 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 81 79 83 85 87 89 91 93 95 97 48 98 96 94 92 90 88 44 84 82 80 78 76 74 72 70 68 66 64 62 60 9 56 54 52 50 99 46 86 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0",
"output": "96"
},
{
"input": "100\n32 47 74 8 14 4 12 68 18 0 44 80 14 38 6 57 4 72 69 3 21 78 74 22 39 32 58 63 34 33 23 6 39 11 6 12 18 4 0 11 20 28 16 1 22 12 57 55 13 48 43 1 50 18 87 6 11 45 38 67 37 14 7 56 6 41 1 55 5 73 78 64 38 18 38 8 37 0 18 61 37 58 58 62 86 5 0 2 15 43 34 61 2 21 15 9 69 1 11 24",
"output": "4"
},
{
"input": "100\n40 3 55 7 6 77 13 46 17 64 21 54 25 27 91 41 1 15 37 82 23 43 42 47 26 95 53 5 11 59 61 9 78 67 69 58 73 0 36 79 60 83 2 87 63 33 71 89 97 99 98 93 56 92 19 88 86 84 39 28 65 20 34 76 51 94 66 12 62 49 96 72 24 52 48 50 44 35 74 31 38 57 81 32 22 80 70 29 30 18 68 16 14 90 10 8 85 4 45 75",
"output": "75"
},
{
"input": "100\n34 16 42 21 84 27 11 7 82 16 95 39 36 64 26 0 38 37 2 2 16 56 16 61 55 42 26 5 61 8 30 20 19 15 9 78 5 34 15 0 3 17 36 36 1 5 4 26 18 0 14 25 7 5 91 7 43 26 79 37 17 27 40 55 66 7 0 2 16 23 68 35 2 5 9 21 1 7 2 9 4 3 22 15 27 6 0 47 5 0 12 9 20 55 36 10 6 8 5 1",
"output": "3"
},
{
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"output": "67"
},
{
"input": "99\n89 96 56 31 32 14 9 66 87 34 69 5 92 54 41 52 46 30 22 26 16 18 20 68 62 73 90 43 79 33 58 98 37 45 10 78 94 51 19 0 91 39 28 47 17 86 3 61 77 7 15 64 55 83 65 71 97 88 6 48 24 11 8 42 81 4 63 93 50 74 35 12 95 27 53 82 29 85 84 60 72 40 36 57 23 13 38 59 49 1 75 44 76 2 21 25 70 80 67",
"output": "75"
},
{
"input": "99\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70 68 66 64 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0",
"output": "98"
},
{
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"output": "22"
},
{
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"output": "96"
},
{
"input": "99\n22 3 19 13 65 87 28 17 41 40 31 21 8 37 29 65 65 53 16 33 13 5 76 4 72 9 2 76 57 72 50 15 75 0 30 13 83 36 12 31 49 51 65 22 48 31 60 15 2 17 6 1 8 0 1 63 3 16 7 7 2 1 47 28 26 21 2 36 1 5 20 25 44 0 2 39 46 30 33 11 15 34 34 4 84 52 0 39 7 3 17 15 6 38 52 64 26 1 0",
"output": "3"
},
{
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"output": "74"
},
{
"input": "99\n22 14 0 44 6 17 6 6 37 45 0 48 19 8 57 8 10 0 3 12 25 2 5 53 9 49 15 6 38 14 9 40 38 22 27 12 64 10 11 35 89 19 46 39 12 24 48 0 52 1 27 27 24 4 64 24 5 0 67 3 5 39 0 1 13 37 2 8 46 1 28 70 6 79 14 15 33 6 7 34 6 18 4 71 1 55 33 71 18 11 47 23 72 53 65 32 2 7 28",
"output": "3"
},
{
"input": "99\n28 59 73 89 52 27 0 20 36 12 83 95 31 24 54 94 49 14 51 34 50 93 13 1 2 68 63 48 41 81 23 43 18 9 16 38 33 60 62 3 40 85 72 69 90 98 11 37 22 44 35 6 21 39 82 10 64 66 96 42 74 30 8 67 97 46 84 32 17 57 75 71 5 26 4 55 58 29 7 15 45 19 92 91 78 65 88 25 86 80 77 87 79 53 47 70 56 76 61",
"output": "63"
}
] | 264 | 204,800 | 3 | 13,926 |
|
68 | Energy exchange | [
"binary search"
] | B. Energy exchange | 2 | 256 | It is well known that the planet suffers from the energy crisis. Little Petya doesn't like that and wants to save the world. For this purpose he needs every accumulator to contain the same amount of energy. Initially every accumulator has some amount of energy: the *i*-th accumulator has *a**i* units of energy. Energy can be transferred from one accumulator to the other. Every time *x* units of energy are transferred (*x* is not necessarily an integer) *k* percent of it is lost. That is, if *x* units were transferred from one accumulator to the other, amount of energy in the first one decreased by *x* units and in other increased by units.
Your task is to help Petya find what maximum equal amount of energy can be stored in each accumulator after the transfers. | First line of the input contains two integers *n* and *k* (1<=≤<=*n*<=≤<=10000,<=0<=≤<=*k*<=≤<=99) — number of accumulators and the percent of energy that is lost during transfers.
Next line contains *n* integers *a*1,<=*a*2,<=... ,<=*a**n* — amounts of energy in the first, second, .., *n*-th accumulator respectively (0<=≤<=*a**i*<=≤<=1000,<=1<=≤<=*i*<=≤<=*n*). | Output maximum possible amount of energy that can remain in each of accumulators after the transfers of energy.
The absolute or relative error in the answer should not exceed 10<=-<=6. | [
"3 50\n4 2 1\n",
"2 90\n1 11\n"
] | [
"2.000000000\n",
"1.909090909\n"
] | none | [
{
"input": "3 50\n4 2 1",
"output": "2.000000000"
},
{
"input": "2 90\n1 11",
"output": "1.909090909"
},
{
"input": "5 26\n42 65 23 43 64",
"output": "45.415178571"
},
{
"input": "5 45\n964 515 454 623 594",
"output": "594.109756098"
},
{
"input": "1 20\n784",
"output": "784.000000000"
},
{
"input": "10 20\n812 896 36 596 709 641 679 778 738 302",
"output": "597.255813953"
},
{
"input": "10 83\n689 759 779 927 15 231 976 943 604 917",
"output": "406.839285714"
},
{
"input": "11 1\n235 280 196 670 495 379 391 280 847 875 506",
"output": "467.586301370"
},
{
"input": "12 71\n472 111 924 103 975 527 807 618 400 523 607 424",
"output": "413.249554367"
},
{
"input": "13 89\n19 944 341 846 764 676 222 957 953 481 708 920 950",
"output": "361.924390244"
},
{
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"output": "523.427098675"
},
{
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"output": "179.075000000"
},
{
"input": "101 71\n113 551 568 26 650 547 89 668 64 651 110 515 482 401 170 971 623 672 135 106 985 751 286 255 82 588 122 568 751 867 335 488 324 122 829 256 675 471 255 723 630 802 667 665 206 774 573 499 361 202 620 522 72 220 739 868 101 135 254 519 896 227 224 968 263 826 466 377 360 24 124 874 877 513 130 79 630 786 265 150 232 783 449 914 815 557 646 367 733 576 840 683 417 709 569 432 515 702 811 877 286",
"output": "343.047284817"
},
{
"input": "102 99\n73 348 420 956 955 436 69 714 87 480 102 555 933 215 452 167 157 593 863 816 337 471 371 574 862 967 581 543 330 348 221 640 378 250 500 428 866 379 1 723 880 992 9 419 0 163 800 96 16 25 19 513 653 19 924 144 135 950 449 481 255 582 844 473 189 841 862 520 242 210 573 381 130 820 357 911 884 735 460 428 764 187 344 760 413 636 868 780 123 614 822 869 792 66 636 843 465 449 191 891 819 30",
"output": "68.702920443"
},
{
"input": "103 26\n33 455 273 884 569 636 360 69 802 310 405 594 693 339 43 53 692 514 590 835 1000 191 456 582 641 35 731 207 600 830 416 483 431 377 481 910 367 597 58 413 128 873 42 173 104 553 26 383 673 849 728 503 924 819 108 422 169 454 333 134 926 247 464 289 115 547 567 663 123 396 21 890 385 436 584 432 829 683 345 706 294 901 238 606 12 24 89 882 203 962 804 745 166 425 393 252 415 195 571 596 41 486 445",
"output": "419.922659430"
},
{
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"output": "399.430903462"
}
] | 310 | 22,323,200 | 3.88092 | 13,984 |
958 | Encryption (easy) | [
"brute force"
] | null | null | Rebel spy Heidi has just obtained the plans for the Death Star from the Empire and, now on her way to safety, she is trying to break the encryption of the plans (of course they are encrypted – the Empire may be evil, but it is not stupid!). The encryption has several levels of security, and here is how the first one looks.
Heidi is presented with a screen that shows her a sequence of integers *A* and a positive integer *p*. She knows that the encryption code is a single number *S*, which is defined as follows:
Define the score of *X* to be the sum of the elements of *X* modulo *p*.
Heidi is given a sequence *A* that consists of *N* integers, and also given an integer *p*. She needs to split *A* into 2 parts such that:
- Each part contains at least 1 element of *A*, and each part consists of contiguous elements of *A*. - The two parts do not overlap. - The total sum *S* of the scores of those two parts is maximized. This is the encryption code.
Output the sum *S*, which is the encryption code. | The first line of the input contains two space-separated integer *N* and *p* (2<=≤<=*N*<=≤<=100<=000, 2<=≤<=*p*<=≤<=10<=000) – the number of elements in *A*, and the modulo for computing scores, respectively.
The second line contains *N* space-separated integers which are the elements of *A*. Each integer is from the interval [1,<=1<=000<=000]. | Output the number *S* as described in the problem statement. | [
"4 10\n3 4 7 2\n",
"10 12\n16 3 24 13 9 8 7 5 12 12\n"
] | [
"16\n",
"13\n"
] | In the first example, the score is maximized if the input sequence is split into two parts as (3, 4), (7, 2). It gives the total score of <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/fc1f9aecea625f3be9a56917d3ba448d669ff278.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
In the second example, the score is maximized if the first part consists of the first three elements, and the second part consists of the rest. Then, the score is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ffd0a0f4c65b0578601ae2fe11a80aec5192f53d.png" style="max-width: 100.0%;max-height: 100.0%;"/>. | [
{
"input": "4 10\n3 4 7 2",
"output": "16"
},
{
"input": "10 12\n16 3 24 13 9 8 7 5 12 12",
"output": "13"
},
{
"input": "2 2\n9 9",
"output": "2"
},
{
"input": "2 2\n8 8",
"output": "0"
},
{
"input": "5 50\n1 1 1 1 1",
"output": "5"
},
{
"input": "5 50\n100 150 200 100 50",
"output": "0"
}
] | 1,000 | 921,600 | 0 | 14,012 |
|
690 | The Wall (easy) | [] | null | null | "The zombies are lurking outside. Waiting. Moaning. And when they come..."
"When they come?"
"I hope the Wall is high enough."
Zombie attacks have hit the Wall, our line of defense in the North. Its protection is failing, and cracks are showing. In places, gaps have appeared, splitting the wall into multiple segments. We call on you for help. Go forth and explore the wall! Report how many disconnected segments there are.
The wall is a two-dimensional structure made of bricks. Each brick is one unit wide and one unit high. Bricks are stacked on top of each other to form columns that are up to *R* bricks high. Each brick is placed either on the ground or directly on top of another brick. Consecutive non-empty columns form a wall segment. The entire wall, all the segments and empty columns in-between, is *C* columns wide. | The first line of the input consists of two space-separated integers *R* and *C*, 1<=≤<=*R*,<=*C*<=≤<=100. The next *R* lines provide a description of the columns as follows:
- each of the *R* lines contains a string of length *C*, - the *c*-th character of line *r* is B if there is a brick in column *c* and row *R*<=-<=*r*<=+<=1, and . otherwise. | The number of wall segments in the input configuration. | [
"3 7\n.......\n.......\n.BB.B..\n",
"4 5\n..B..\n..B..\nB.B.B\nBBB.B\n",
"4 6\n..B...\nB.B.BB\nBBB.BB\nBBBBBB\n",
"1 1\nB\n",
"10 7\n.......\n.......\n.......\n.......\n.......\n.......\n.......\n.......\n...B...\nB.BB.B.\n",
"8 8\n........\n........\n........\n........\n.B......\n.B.....B\n.B.....B\n.BB...BB\n"
] | [
"2\n",
"2\n",
"1\n",
"1\n",
"3\n",
"2\n"
] | In the first sample case, the 2nd and 3rd columns define the first wall segment, and the 5th column defines the second. | [
{
"input": "3 7\n.......\n.......\n.BB.B..",
"output": "2"
},
{
"input": "4 5\n..B..\n..B..\nB.B.B\nBBB.B",
"output": "2"
},
{
"input": "4 6\n..B...\nB.B.BB\nBBB.BB\nBBBBBB",
"output": "1"
},
{
"input": "1 1\nB",
"output": "1"
},
{
"input": "10 7\n.......\n.......\n.......\n.......\n.......\n.......\n.......\n.......\n...B...\nB.BB.B.",
"output": "3"
},
{
"input": "8 8\n........\n........\n........\n........\n.B......\n.B.....B\n.B.....B\n.BB...BB",
"output": "2"
}
] | 93 | 6,758,400 | 3 | 14,038 |
|
592 | Super M | [
"dfs and similar",
"dp",
"graphs",
"trees"
] | null | null | Ari the monster is not an ordinary monster. She is the hidden identity of Super M, the Byteforces’ superhero. Byteforces is a country that consists of *n* cities, connected by *n*<=-<=1 bidirectional roads. Every road connects exactly two distinct cities, and the whole road system is designed in a way that one is able to go from any city to any other city using only the given roads. There are *m* cities being attacked by humans. So Ari... we meant Super M have to immediately go to each of the cities being attacked to scare those bad humans. Super M can pass from one city to another only using the given roads. Moreover, passing through one road takes her exactly one kron - the time unit used in Byteforces.
However, Super M is not on Byteforces now - she is attending a training camp located in a nearby country Codeforces. Fortunately, there is a special device in Codeforces that allows her to instantly teleport from Codeforces to any city of Byteforces. The way back is too long, so for the purpose of this problem teleportation is used exactly once.
You are to help Super M, by calculating the city in which she should teleport at the beginning in order to end her job in the minimum time (measured in krons). Also, provide her with this time so she can plan her way back to Codeforces. | The first line of the input contains two integers *n* and *m* (1<=≤<=*m*<=≤<=*n*<=≤<=123456) - the number of cities in Byteforces, and the number of cities being attacked respectively.
Then follow *n*<=-<=1 lines, describing the road system. Each line contains two city numbers *u**i* and *v**i* (1<=≤<=*u**i*,<=*v**i*<=≤<=*n*) - the ends of the road *i*.
The last line contains *m* distinct integers - numbers of cities being attacked. These numbers are given in no particular order. | First print the number of the city Super M should teleport to. If there are many possible optimal answers, print the one with the lowest city number.
Then print the minimum possible time needed to scare all humans in cities being attacked, measured in Krons.
Note that the correct answer is always unique. | [
"7 2\n1 2\n1 3\n1 4\n3 5\n3 6\n3 7\n2 7\n",
"6 4\n1 2\n2 3\n2 4\n4 5\n4 6\n2 4 5 6\n"
] | [
"2\n3\n",
"2\n4\n"
] | In the first sample, there are two possibilities to finish the Super M's job in 3 krons. They are:
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/93d3c0306b529e9c2324f68158ca2156587473a2.png" style="max-width: 100.0%;max-height: 100.0%;"/> and <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/df80aa84591eaa7b9f52c88cc43b5f7da5bfead3.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
However, you should choose the first one as it starts in the city with the lower number. | [
{
"input": "7 2\n1 2\n1 3\n1 4\n3 5\n3 6\n3 7\n2 7",
"output": "2\n3"
},
{
"input": "6 4\n1 2\n2 3\n2 4\n4 5\n4 6\n2 4 5 6",
"output": "2\n4"
},
{
"input": "2 1\n2 1\n1",
"output": "1\n0"
},
{
"input": "1 1\n1",
"output": "1\n0"
},
{
"input": "10 2\n6 9\n6 2\n1 6\n4 10\n3 7\n9 4\n9 5\n6 7\n2 8\n7 6",
"output": "6\n1"
},
{
"input": "15 2\n7 12\n13 11\n6 8\n2 15\n10 9\n5 1\n13 5\n5 4\n14 3\n8 9\n8 4\n4 7\n12 14\n5 2\n7 4",
"output": "4\n1"
},
{
"input": "20 2\n1 16\n12 5\n15 19\n18 9\n8 4\n10 16\n9 16\n20 15\n14 19\n7 4\n18 12\n17 12\n2 20\n6 14\n3 19\n7 19\n18 15\n19 13\n9 11\n12 18",
"output": "12\n1"
},
{
"input": "4 2\n4 3\n3 1\n1 2\n3 4",
"output": "3\n1"
},
{
"input": "8 5\n2 5\n1 8\n6 7\n3 4\n6 8\n8 5\n5 3\n1 6 7 3 8",
"output": "3\n6"
},
{
"input": "16 8\n16 12\n16 15\n15 9\n15 13\n16 3\n15 2\n15 10\n1 2\n6 16\n5 15\n2 7\n15 4\n14 15\n11 16\n8 5\n5 10 14 6 8 3 1 9",
"output": "1\n16"
},
{
"input": "32 28\n30 12\n30 27\n24 32\n6 13\n11 5\n4 30\n8 28\n9 20\n8 20\n7 20\n5 30\n18 5\n20 14\n23 20\n17 20\n8 26\n20 1\n15 2\n20 13\n24 20\n22 24\n25 16\n2 3\n19 5\n16 10\n31 2\n29 5\n20 16\n2 20\n5 21\n5 20\n32 11 6 12 22 30 23 21 14 13 1 20 7 25 9 29 10 27 5 19 24 31 15 26 8 3 28 17",
"output": "3\n53"
},
{
"input": "10 3\n10 5\n3 2\n6 8\n1 5\n10 4\n6 1\n9 8\n2 9\n7 3\n3 9 1",
"output": "1\n5"
},
{
"input": "7 5\n6 4\n5 6\n6 7\n2 3\n5 2\n2 1\n4 6 1 7 3",
"output": "1\n8"
},
{
"input": "15 7\n5 4\n12 5\n7 13\n10 11\n3 8\n6 12\n3 15\n1 3\n5 14\n7 9\n1 10\n6 1\n12 7\n10 2\n4 10 8 13 1 7 9",
"output": "4\n14"
},
{
"input": "31 16\n3 25\n8 1\n1 9\n1 23\n16 15\n10 6\n25 30\n20 29\n2 24\n3 7\n19 22\n2 12\n16 4\n7 26\n31 10\n17 13\n25 21\n7 18\n28 2\n6 27\n19 5\n13 3\n17 31\n10 16\n20 14\n8 19\n6 11\n28 20\n13 28\n31 8\n31 27 25 20 26 8 28 15 18 17 10 23 4 16 30 22",
"output": "4\n34"
},
{
"input": "63 20\n35 26\n54 5\n32 56\n56 53\n59 46\n37 31\n46 8\n4 1\n2 47\n59 42\n55 11\n62 6\n30 7\n60 24\n41 36\n34 22\n24 34\n21 2\n12 52\n8 44\n60 21\n24 30\n48 35\n48 25\n32 57\n20 37\n11 54\n11 62\n42 58\n31 43\n12 23\n55 48\n51 55\n41 27\n25 33\n21 18\n42 12\n4 15\n51 60\n62 39\n46 41\n57 9\n30 61\n31 4\n58 13\n34 29\n37 32\n18 16\n57 45\n2 49\n40 51\n43 17\n40 20\n20 59\n8 19\n58 10\n43 63\n54 50\n18 14\n25 38\n56 28\n35 3\n41 36 18 28 54 22 20 6 23 38 33 52 48 44 29 56 63 4 27 50",
"output": "6\n66"
},
{
"input": "4 2\n2 3\n2 1\n2 4\n3 4",
"output": "3\n2"
},
{
"input": "13 11\n4 11\n2 7\n4 13\n8 12\n8 9\n8 6\n3 8\n4 1\n2 10\n2 5\n3 4\n3 2\n10 4 5 6 1 2 3 9 13 7 12",
"output": "1\n18"
},
{
"input": "7 5\n1 5\n4 1\n1 3\n7 1\n1 6\n1 2\n2 4 1 3 7",
"output": "2\n6"
},
{
"input": "12 9\n11 12\n1 10\n1 7\n5 6\n8 7\n9 8\n4 5\n1 4\n2 3\n1 2\n10 11\n4 9 11 3 5 12 8 6 7",
"output": "6\n16"
},
{
"input": "56 34\n7 31\n47 6\n13 4\n51 29\n13 12\n10 52\n10 41\n1 47\n47 54\n9 1\n4 27\n4 40\n49 19\n21 26\n24 33\n56 49\n41 56\n7 23\n41 48\n16 34\n35 9\n56 51\n5 43\n44 46\n10 25\n49 2\n1 21\n9 32\n33 20\n16 5\n5 35\n55 50\n55 53\n37 44\n43 15\n4 55\n8 10\n8 24\n21 42\n37 8\n39 13\n49 38\n39 16\n50 3\n55 7\n51 45\n21 11\n51 28\n50 18\n50 30\n5 37\n7 17\n35 22\n47 36\n35 14\n3 38 47 22 34 10 54 50 9 52 36 1 21 29 28 6 13 39 4 40 53 51 35 55 45 18 44 20 42 31 11 46 41 12",
"output": "3\n70"
},
{
"input": "26 22\n20 16\n2 7\n7 19\n5 9\n20 23\n22 18\n24 3\n8 22\n16 10\n5 2\n7 15\n22 14\n25 4\n25 11\n24 13\n8 24\n13 1\n20 8\n22 6\n7 26\n16 12\n16 5\n13 21\n25 17\n2 25\n16 4 7 24 10 12 2 23 20 1 26 14 8 9 3 6 21 13 11 18 22 17",
"output": "1\n37"
},
{
"input": "43 13\n7 28\n17 27\n39 8\n21 3\n17 20\n17 2\n9 6\n35 23\n43 22\n7 41\n5 24\n26 11\n21 43\n41 17\n16 5\n25 15\n39 10\n18 7\n37 33\n39 13\n39 16\n10 12\n1 21\n2 25\n14 36\n12 7\n16 34\n24 4\n25 40\n5 29\n37 31\n3 32\n22 14\n16 35\n5 37\n10 38\n25 19\n9 1\n26 42\n43 26\n10 30\n33 9\n28 6 42 38 27 32 8 11 36 7 41 29 19",
"output": "19\n41"
},
{
"input": "21 20\n16 9\n7 11\n4 12\n2 17\n17 7\n5 2\n2 8\n4 10\n8 19\n6 15\n2 6\n12 18\n16 5\n20 16\n6 14\n5 3\n5 21\n20 1\n17 13\n6 4\n6 4 18 11 14 1 19 15 10 8 9 17 16 3 20 13 2 5 12 21",
"output": "1\n32"
},
{
"input": "29 6\n16 9\n20 13\n24 3\n24 28\n22 12\n10 11\n10 26\n22 4\n10 27\n5 1\n2 23\n23 5\n16 7\n8 24\n7 19\n19 17\n8 10\n20 16\n20 25\n24 20\n23 15\n22 29\n2 8\n7 22\n2 21\n23 14\n19 18\n19 6\n19 17 18 27 29 4",
"output": "4\n16"
},
{
"input": "31 29\n10 14\n16 6\n23 22\n25 23\n2 27\n24 17\n20 8\n5 2\n8 24\n16 5\n10 26\n8 7\n5 29\n20 16\n13 9\n13 21\n24 30\n13 1\n10 15\n23 3\n25 10\n2 25\n20 13\n25 11\n8 12\n30 28\n20 18\n5 4\n23 19\n16 31\n13 14 3 30 5 6 26 22 25 1 23 7 31 12 16 28 17 2 8 18 24 4 20 21 15 11 9 29 10",
"output": "3\n46"
},
{
"input": "54 8\n33 9\n39 36\n22 14\n24 13\n8 50\n34 52\n47 2\n35 44\n16 54\n34 25\n1 3\n39 11\n9 17\n43 19\n10 40\n47 38\n5 37\n21 47\n37 12\n16 6\n37 7\n32 26\n39 42\n44 10\n1 18\n37 8\n9 1\n8 24\n10 33\n33 53\n5 4\n21 30\n9 31\n24 28\n24 49\n16 5\n34 35\n21 48\n47 43\n13 34\n39 16\n10 27\n22 32\n43 22\n13 46\n33 23\n44 15\n1 21\n8 41\n43 45\n5 29\n35 20\n13 51\n40 50 33 14 48 25 44 9",
"output": "14\n21"
},
{
"input": "17 12\n5 2\n4 3\n8 17\n2 4\n2 8\n17 12\n8 10\n6 11\n16 7\n4 14\n15 13\n6 9\n4 6\n15 16\n16 5\n9 1\n4 8 1 9 3 12 15 10 13 6 14 16",
"output": "1\n20"
},
{
"input": "28 6\n25 21\n9 18\n25 1\n16 5\n9 11\n28 19\n5 2\n20 16\n20 13\n2 23\n5 25\n8 24\n14 27\n3 15\n24 28\n8 10\n22 14\n14 17\n13 9\n3 22\n22 26\n16 7\n2 8\n25 3\n3 12\n14 4\n9 6\n28 27 22 24 20 16",
"output": "27\n13"
},
{
"input": "10 9\n3 9\n4 8\n10 1\n2 3\n5 6\n4 3\n1 2\n5 4\n6 7\n9 1 5 8 7 3 4 6 10",
"output": "7\n11"
},
{
"input": "9 6\n1 6\n3 4\n9 7\n3 2\n8 7\n2 1\n6 7\n3 5\n2 5 1 6 3 9",
"output": "5\n6"
},
{
"input": "19 11\n8 9\n10 13\n16 15\n6 4\n3 2\n17 16\n4 7\n1 14\n10 11\n15 14\n4 3\n10 12\n4 5\n2 1\n16 19\n8 1\n10 9\n18 16\n10 14 18 12 17 11 19 8 1 3 9",
"output": "11\n18"
},
{
"input": "36 5\n36 33\n11 12\n14 12\n25 24\n27 26\n23 24\n20 19\n1 2\n3 2\n17 18\n33 34\n23 1\n32 31\n12 15\n25 26\n4 5\n5 8\n5 6\n26 29\n1 9\n35 33\n33 32\n16 1\n3 4\n31 30\n16 17\n19 21\n1 30\n7 5\n9 10\n13 12\n19 18\n10 11\n22 19\n28 26\n29 12 11 17 33",
"output": "12\n21"
},
{
"input": "10 2\n5 1\n1 3\n3 4\n4 2\n5 10\n1 9\n3 8\n4 7\n2 6\n3 4",
"output": "3\n1"
},
{
"input": "53 30\n41 42\n27 24\n13 11\n10 11\n32 33\n34 33\n37 40\n21 22\n21 20\n46 47\n2 1\n31 30\n29 30\n11 14\n42 43\n50 51\n34 35\n36 35\n24 23\n48 47\n41 1\n28 29\n45 44\n16 15\n5 4\n6 5\n18 19\n9 8\n37 38\n11 12\n39 37\n49 48\n50 49\n43 44\n50 53\n3 4\n50 52\n24 25\n7 6\n46 45\n2 3\n17 18\n31 32\n19 20\n7 8\n15 1\n36 37\n23 22\n9 10\n17 16\n24 26\n28 1\n38 52 41 35 53 43 3 29 36 4 23 20 46 5 40 30 49 25 16 48 17 27 21 9 45 44 15 13 14 2",
"output": "13\n74"
},
{
"input": "10 4\n2 3\n4 2\n8 9\n6 5\n8 1\n5 1\n8 10\n7 5\n1 2\n4 10 2 5",
"output": "4\n6"
},
{
"input": "10 5\n4 5\n9 1\n1 2\n7 1\n5 1\n10 1\n7 3\n6 3\n5 8\n5 2 7 10 1",
"output": "2\n6"
},
{
"input": "10 4\n8 7\n7 6\n1 2\n3 2\n3 4\n6 5\n10 7\n7 9\n5 4\n9 5 10 4",
"output": "4\n6"
},
{
"input": "5 4\n2 3\n2 1\n3 5\n4 3\n4 2 5 1",
"output": "1\n5"
},
{
"input": "5 1\n1 2\n2 3\n3 4\n4 5\n4",
"output": "4\n0"
}
] | 1,778 | 268,390,400 | 0 | 14,074 |
|
847 | Sum of Nestings | [
"constructive algorithms"
] | null | null | Recall that the bracket sequence is considered regular if it is possible to insert symbols '+' and '1' into it so that the result is a correct arithmetic expression. For example, a sequence "(()())" is regular, because we can get correct arithmetic expression insering symbols '+' and '1': "((1+1)+(1+1))". Also the following sequences are regular: "()()()", "(())" and "()". The following sequences are not regular bracket sequences: ")(", "(()" and "())(()".
In this problem you are given two integers *n* and *k*. Your task is to construct a regular bracket sequence consisting of round brackets with length 2·*n* with total sum of nesting of all opening brackets equals to exactly *k*. The nesting of a single opening bracket equals to the number of pairs of brackets in which current opening bracket is embedded.
For example, in the sequence "()(())" the nesting of first opening bracket equals to 0, the nesting of the second opening bracket equals to 0 and the nesting of the third opening bracket equal to 1. So the total sum of nestings equals to 1. | The first line contains two integers *n* and *k* (1<=≤<=*n*<=≤<=3·105, 0<=≤<=*k*<=≤<=1018) — the number of opening brackets and needed total nesting. | Print the required regular bracket sequence consisting of round brackets.
If there is no solution print "Impossible" (without quotes). | [
"3 1\n",
"4 6\n",
"2 5\n"
] | [
"()(())",
"(((())))",
"Impossible\n"
] | The first example is examined in the statement.
In the second example the answer is "(((())))". The nesting of the first opening bracket is 0, the nesting of the second is 1, the nesting of the third is 2, the nesting of fourth is 3. So the total sum of nestings equals to 0 + 1 + 2 + 3 = 6.
In the third it is impossible to construct a regular bracket sequence, because the maximum possible total sum of nestings for two opening brackets equals to 1. This total sum of nestings is obtained for the sequence "(())". | [
{
"input": "3 1",
"output": "()(())"
},
{
"input": "4 6",
"output": "(((())))"
},
{
"input": "2 5",
"output": "Impossible"
},
{
"input": "1 0",
"output": "()"
},
{
"input": "2 0",
"output": "()()"
},
{
"input": "2 1",
"output": "(())"
},
{
"input": "3 0",
"output": "()()()"
},
{
"input": "10 42",
"output": "(((((((()()())))))))"
},
{
"input": "3 2",
"output": "(()())"
},
{
"input": "3 3",
"output": "((()))"
},
{
"input": "4 1",
"output": "()()(())"
},
{
"input": "4 2",
"output": "()(()())"
},
{
"input": "4 0",
"output": "()()()()"
},
{
"input": "4 3",
"output": "(()()())"
},
{
"input": "4 4",
"output": "(()(()))"
},
{
"input": "4 5",
"output": "((()()))"
},
{
"input": "20 132",
"output": "((((((()(((()()()()()()()()()())))))))))"
},
{
"input": "5 0",
"output": "()()()()()"
},
{
"input": "5 1",
"output": "()()()(())"
},
{
"input": "5 2",
"output": "()()(()())"
},
{
"input": "5 3",
"output": "()(()()())"
},
{
"input": "5 4",
"output": "(()()()())"
},
{
"input": "5 5",
"output": "()((()()))"
},
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},
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"input": "300000 44754406973",
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},
{
"input": "300000 44999849986",
"output": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((..."
},
{
"input": "10 48",
"output": "Impossible"
},
{
"input": "100 4952",
"output": "Impossible"
},
{
"input": "1000 499505",
"output": "Impossible"
},
{
"input": "5001 12502504",
"output": "Impossible"
},
{
"input": "9999 49985003",
"output": "Impossible"
},
{
"input": "300000 44999850003",
"output": "Impossible"
},
{
"input": "10 46",
"output": "Impossible"
},
{
"input": "100 4955",
"output": "Impossible"
},
{
"input": "1000 499503",
"output": "Impossible"
},
{
"input": "5001 12502503",
"output": "Impossible"
},
{
"input": "9999 49985002",
"output": "Impossible"
},
{
"input": "300000 44999850002",
"output": "Impossible"
},
{
"input": "300000 1000000000000000000",
"output": "Impossible"
},
{
"input": "300000 44999850000",
"output": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((..."
},
{
"input": "300000 44999850001",
"output": "Impossible"
},
{
"input": "300000 44999849999",
"output": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((..."
},
{
"input": "300000 44999849998",
"output": "(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((..."
},
{
"input": "300000 44999849997",
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},
{
"input": "300000 0",
"output": "()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(..."
},
{
"input": "300000 1",
"output": "()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(..."
},
{
"input": "300000 2",
"output": "()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(..."
},
{
"input": "300000 3",
"output": "()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(..."
},
{
"input": "1 1",
"output": "Impossible"
},
{
"input": "1 2",
"output": "Impossible"
},
{
"input": "1 1000000000000000000",
"output": "Impossible"
},
{
"input": "2 2",
"output": "Impossible"
},
{
"input": "2 3",
"output": "Impossible"
},
{
"input": "300000 14999849999",
"output": "()()(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((..."
},
{
"input": "2 1000000000000000000",
"output": "Impossible"
},
{
"input": "299999 1000000000000000000",
"output": "Impossible"
}
] | 2,000 | 6,451,200 | 0 | 14,090 |
|
250 | Building Bridge | [
"geometry",
"ternary search",
"two pointers"
] | null | null | Two villages are separated by a river that flows from the north to the south. The villagers want to build a bridge across the river to make it easier to move across the villages.
The river banks can be assumed to be vertical straight lines *x*<==<=*a* and *x*<==<=*b* (0<=<<=*a*<=<<=*b*).
The west village lies in a steppe at point *O*<==<=(0,<=0). There are *n* pathways leading from the village to the river, they end at points *A**i*<==<=(*a*,<=*y**i*). The villagers there are plain and simple, so their pathways are straight segments as well.
The east village has reserved and cunning people. Their village is in the forest on the east bank of the river, but its exact position is not clear. There are *m* twisted paths leading from this village to the river and ending at points *B**i*<==<=(*b*,<=*y*'*i*). The lengths of all these paths are known, the length of the path that leads from the eastern village to point *B**i*, equals *l**i*.
The villagers want to choose exactly one point on the left bank of river *A**i*, exactly one point on the right bank *B**j* and connect them by a straight-line bridge so as to make the total distance between the villages (the sum of |*OA**i*|<=+<=|*A**i**B**j*|<=+<=*l**j*, where |*XY*| is the Euclidean distance between points *X* and *Y*) were minimum. The Euclidean distance between points (*x*1,<=*y*1) and (*x*2,<=*y*2) equals .
Help them and find the required pair of points. | The first line contains integers *n*, *m*, *a*, *b* (1<=≤<=*n*,<=*m*<=≤<=105, 0<=<<=*a*<=<<=*b*<=<<=106).
The second line contains *n* integers in the ascending order: the *i*-th integer determines the coordinate of point *A**i* and equals *y**i* (|*y**i*|<=≤<=106).
The third line contains *m* integers in the ascending order: the *i*-th integer determines the coordinate of point *B**i* and equals *y*'*i* (|*y*'*i*|<=≤<=106).
The fourth line contains *m* more integers: the *i*-th of them determines the length of the path that connects the eastern village and point *B**i*, and equals *l**i* (1<=≤<=*l**i*<=≤<=106).
It is guaranteed, that there is such a point *C* with abscissa at least *b*, that |*B**i**C*|<=≤<=*l**i* for all *i* (1<=≤<=*i*<=≤<=*m*). It is guaranteed that no two points *A**i* coincide. It is guaranteed that no two points *B**i* coincide. | Print two integers — the numbers of points on the left (west) and right (east) banks, respectively, between which you need to build a bridge. You can assume that the points on the west bank are numbered from 1 to *n*, in the order in which they are given in the input. Similarly, the points on the east bank are numbered from 1 to *m* in the order in which they are given in the input.
If there are multiple solutions, print any of them. The solution will be accepted if the final length of the path will differ from the answer of the jury by no more than 10<=-<=6 in absolute or relative value. | [
"3 2 3 5\n-2 -1 4\n-1 2\n7 3\n"
] | [
"2 2"
] | none | [
{
"input": "3 2 3 5\n-2 -1 4\n-1 2\n7 3",
"output": "2 2"
},
{
"input": "1 1 10 20\n5\n-5\n1",
"output": "1 1"
},
{
"input": "2 2 1 2\n-1 10\n8 9\n3 7",
"output": "1 1"
},
{
"input": "10 20 50 60\n-96 -75 32 37 42 43 44 57 61 65\n-95 -90 -86 -79 -65 -62 -47 -11 -8 -6 1 8 23 25 32 51 73 88 94 100\n138 75 132 116 49 43 96 166 96 161 146 112 195 192 201 186 251 254 220 227",
"output": "2 6"
}
] | 78 | 307,200 | 0 | 14,114 |
|
798 | Mike and gcd problem | [
"dp",
"greedy",
"number theory"
] | null | null | Mike has a sequence *A*<==<=[*a*1,<=*a*2,<=...,<=*a**n*] of length *n*. He considers the sequence *B*<==<=[*b*1,<=*b*2,<=...,<=*b**n*] beautiful if the *gcd* of all its elements is bigger than 1, i.e. .
Mike wants to change his sequence in order to make it beautiful. In one move he can choose an index *i* (1<=≤<=*i*<=<<=*n*), delete numbers *a**i*,<=*a**i*<=+<=1 and put numbers *a**i*<=-<=*a**i*<=+<=1,<=*a**i*<=+<=*a**i*<=+<=1 in their place instead, in this order. He wants perform as few operations as possible. Find the minimal number of operations to make sequence *A* beautiful if it's possible, or tell him that it is impossible to do so.
is the biggest non-negative number *d* such that *d* divides *b**i* for every *i* (1<=≤<=*i*<=≤<=*n*). | The first line contains a single integer *n* (2<=≤<=*n*<=≤<=100<=000) — length of sequence *A*.
The second line contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109) — elements of sequence *A*. | Output on the first line "YES" (without quotes) if it is possible to make sequence *A* beautiful by performing operations described above, and "NO" (without quotes) otherwise.
If the answer was "YES", output the minimal number of moves needed to make sequence *A* beautiful. | [
"2\n1 1\n",
"3\n6 2 4\n",
"2\n1 3\n"
] | [
"YES\n1\n",
"YES\n0\n",
"YES\n1\n"
] | In the first example you can simply make one move to obtain sequence [0, 2] with <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6ddb490b8e898198d30c56c6edce2cf15e6f998a.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
In the second example the *gcd* of the sequence is already greater than 1. | [
{
"input": "2\n1 1",
"output": "YES\n1"
},
{
"input": "3\n6 2 4",
"output": "YES\n0"
},
{
"input": "2\n1 3",
"output": "YES\n1"
},
{
"input": "9\n57 30 28 81 88 32 3 42 25",
"output": "YES\n8"
},
{
"input": "2\n8 77",
"output": "YES\n2"
},
{
"input": "4\n92 46 3 21",
"output": "YES\n1"
},
{
"input": "2\n78 26",
"output": "YES\n0"
},
{
"input": "2\n3 6",
"output": "YES\n0"
},
{
"input": "2\n3 9",
"output": "YES\n0"
},
{
"input": "2\n3 3",
"output": "YES\n0"
},
{
"input": "3\n3 6 3",
"output": "YES\n0"
},
{
"input": "3\n3 9 15",
"output": "YES\n0"
},
{
"input": "3\n3 6 9",
"output": "YES\n0"
},
{
"input": "3\n3 3 3",
"output": "YES\n0"
},
{
"input": "3\n3 9 18",
"output": "YES\n0"
},
{
"input": "5\n1 2 1 2 1",
"output": "YES\n6"
},
{
"input": "2\n9 6",
"output": "YES\n0"
},
{
"input": "4\n3 6 9 12",
"output": "YES\n0"
},
{
"input": "3\n3 9 27",
"output": "YES\n0"
},
{
"input": "3\n3 9 12",
"output": "YES\n0"
},
{
"input": "5\n6 6 9 15 21",
"output": "YES\n0"
},
{
"input": "2\n5 15",
"output": "YES\n0"
},
{
"input": "4\n2 3 9 13",
"output": "YES\n3"
},
{
"input": "4\n3 3 3 3",
"output": "YES\n0"
},
{
"input": "5\n3 9 9 9 27",
"output": "YES\n0"
},
{
"input": "2\n9 9",
"output": "YES\n0"
},
{
"input": "3\n3 9 9",
"output": "YES\n0"
},
{
"input": "3\n7 14 21",
"output": "YES\n0"
},
{
"input": "3\n3 12 4",
"output": "YES\n2"
},
{
"input": "5\n3 3 3 3 3",
"output": "YES\n0"
}
] | 46 | 0 | 0 | 14,145 |
|
522 | Chicken or Fish? | [
"greedy"
] | null | null | Polycarp is flying in the airplane. Finally, it is his favorite time — the lunchtime. The BerAvia company stewardess is giving food consecutively to all the passengers from the 1-th one to the last one. Polycarp is sitting on seat *m*, that means, he will be the *m*-th person to get food.
The flight menu has *k* dishes in total and when Polycarp boarded the flight, he had time to count the number of portions of each dish on board. Thus, he knows values *a*1,<=*a*2,<=...,<=*a**k*, where *a**i* is the number of portions of the *i*-th dish.
The stewardess has already given food to *m*<=-<=1 passengers, gave Polycarp a polite smile and asked him what he would prefer. That's when Polycarp realized that they might have run out of some dishes by that moment. For some of the *m*<=-<=1 passengers ahead of him, he noticed what dishes they were given. Besides, he's heard some strange mumbling from some of the *m*<=-<=1 passengers ahead of him, similar to phrase 'I'm disappointed'. That happened when a passenger asked for some dish but the stewardess gave him a polite smile and said that they had run out of that dish. In that case the passenger needed to choose some other dish that was available. If Polycarp heard no more sounds from a passenger, that meant that the passenger chose his dish at the first try.
Help Polycarp to find out for each dish: whether they could have run out of the dish by the moment Polyarp was served or that dish was definitely available. | Each test in this problem consists of one or more input sets. First goes a string that contains a single integer *t* (1<=≤<=*t*<=≤<=100<=000) — the number of input data sets in the test. Then the sets follow, each set is preceded by an empty line.
The first line of each set of the input contains integers *m*, *k* (2<=≤<=*m*<=≤<=100<=000, 1<=≤<=*k*<=≤<=100<=000) — the number of Polycarp's seat and the number of dishes, respectively.
The second line contains a sequence of *k* integers *a*1,<=*a*2,<=...,<=*a**k* (1<=≤<=*a**i*<=≤<=100<=000), where *a**i* is the initial number of portions of the *i*-th dish.
Then *m*<=-<=1 lines follow, each line contains the description of Polycarp's observations about giving food to a passenger sitting in front of him: the *j*-th line contains a pair of integers *t**j*,<=*r**j* (0<=≤<=*t**j*<=≤<=*k*,<=0<=≤<=*r**j*<=≤<=1), where *t**j* is the number of the dish that was given to the *j*-th passenger (or 0, if Polycarp didn't notice what dish was given to the passenger), and *r**j* — a 1 or a 0, depending on whether the *j*-th passenger was or wasn't disappointed, respectively.
We know that sum *a**i* equals at least *m*, that is,Polycarp will definitely get some dish, even if it is the last thing he wanted. It is guaranteed that the data is consistent.
Sum *m* for all input sets doesn't exceed 100<=000. Sum *k* for all input sets doesn't exceed 100<=000. | For each input set print the answer as a single line. Print a string of *k* letters "Y" or "N". Letter "Y" in position *i* should be printed if they could have run out of the *i*-th dish by the time the stewardess started serving Polycarp. | [
"2\n\n3 4\n2 3 2 1\n1 0\n0 0\n\n5 5\n1 2 1 3 1\n3 0\n0 0\n2 1\n4 0\n"
] | [
"YNNY\nYYYNY\n"
] | In the first input set depending on the choice of the second passenger the situation could develop in different ways:
- If he chose the first dish, then by the moment the stewardess reaches Polycarp, they will have run out of the first dish; - If he chose the fourth dish, then by the moment the stewardess reaches Polycarp, they will have run out of the fourth dish; - Otherwise, Polycarp will be able to choose from any of the four dishes.
Thus, the answer is "YNNY".
In the second input set there is, for example, the following possible scenario. First, the first passenger takes the only third dish, then the second passenger takes the second dish. Then, the third passenger asks for the third dish, but it is not available, so he makes disappointed muttering and ends up with the second dish. Then the fourth passenger takes the fourth dish, and Polycarp ends up with the choice between the first, fourth and fifth dish.
Likewise, another possible scenario is when by the time the stewardess comes to Polycarp, they will have run out of either the first or the fifth dish (this can happen if one of these dishes is taken by the second passenger). It is easy to see that there is more than enough of the fourth dish, so Polycarp can always count on it. Thus, the answer is "YYYNY". | [
{
"input": "2\n\n3 4\n2 3 2 1\n1 0\n0 0\n\n5 5\n1 2 1 3 1\n3 0\n0 0\n2 1\n4 0",
"output": "YNNY\nYYYNY"
},
{
"input": "4\n\n2 1\n42\n0 0\n\n2 1\n2\n0 0\n\n2 1\n42\n1 0\n\n2 1\n2\n1 0",
"output": "N\nN\nN\nN"
},
{
"input": "5\n\n3 3\n1 1 1\n0 0\n0 1\n\n3 3\n1 1 1\n1 0\n2 1\n\n3 3\n1 1 1\n1 0\n0 1\n\n3 3\n1 1 1\n0 0\n1 0\n\n3 3\n1 1 1\n0 0\n1 1",
"output": "YYY\nYYN\nYYY\nYYY\nYYY"
},
{
"input": "1\n\n4 2\n2 2\n0 0\n0 0\n1 1",
"output": "NY"
}
] | 61 | 5,632,000 | -1 | 14,174 |
|
246 | Colorful Graph | [
"brute force",
"dfs and similar",
"graphs"
] | null | null | You've got an undirected graph, consisting of *n* vertices and *m* edges. We will consider the graph's vertices numbered with integers from 1 to *n*. Each vertex of the graph has a color. The color of the *i*-th vertex is an integer *c**i*.
Let's consider all vertices of the graph, that are painted some color *k*. Let's denote a set of such as *V*(*k*). Let's denote the value of the neighbouring color diversity for color *k* as the cardinality of the set *Q*(*k*)<==<={*c**u* :<= *c**u*<=≠<=*k* and there is vertex *v* belonging to set *V*(*k*) such that nodes *v* and *u* are connected by an edge of the graph}.
Your task is to find such color *k*, which makes the cardinality of set *Q*(*k*) maximum. In other words, you want to find the color that has the most diverse neighbours. Please note, that you want to find such color *k*, that the graph has at least one vertex with such color. | The first line contains two space-separated integers *n*,<=*m* (1<=≤<=*n*,<=*m*<=≤<=105) — the number of vertices end edges of the graph, correspondingly. The second line contains a sequence of integers *c*1,<=*c*2,<=...,<=*c**n* (1<=≤<=*c**i*<=≤<=105) — the colors of the graph vertices. The numbers on the line are separated by spaces.
Next *m* lines contain the description of the edges: the *i*-th line contains two space-separated integers *a**i*,<=*b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*; *a**i*<=≠<=*b**i*) — the numbers of the vertices, connected by the *i*-th edge.
It is guaranteed that the given graph has no self-loops or multiple edges. | Print the number of the color which has the set of neighbours with the maximum cardinality. It there are multiple optimal colors, print the color with the minimum number. Please note, that you want to find such color, that the graph has at least one vertex with such color. | [
"6 6\n1 1 2 3 5 8\n1 2\n3 2\n1 4\n4 3\n4 5\n4 6\n",
"5 6\n4 2 5 2 4\n1 2\n2 3\n3 1\n5 3\n5 4\n3 4\n"
] | [
"3\n",
"2\n"
] | none | [
{
"input": "6 6\n1 1 2 3 5 8\n1 2\n3 2\n1 4\n4 3\n4 5\n4 6",
"output": "3"
},
{
"input": "5 6\n4 2 5 2 4\n1 2\n2 3\n3 1\n5 3\n5 4\n3 4",
"output": "2"
},
{
"input": "3 1\n13 13 4\n1 2",
"output": "4"
},
{
"input": "2 1\n500 300\n1 2",
"output": "300"
},
{
"input": "6 5\n2 2 2 1 2 2\n4 5\n4 2\n5 2\n4 1\n2 3",
"output": "1"
},
{
"input": "8 8\n3 3 2 3 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n5 6\n4 2\n7 5\n1 6",
"output": "3"
},
{
"input": "10 27\n1 1 3 2 4 1 3 2 4 1\n9 3\n7 8\n9 7\n6 5\n7 6\n7 4\n6 9\n3 8\n6 10\n8 5\n3 1\n4 6\n8 1\n10 8\n9 5\n10 1\n5 10\n3 6\n4 3\n8 2\n10 7\n10 9\n10 3\n8 4\n3 2\n2 4\n6 1",
"output": "1"
},
{
"input": "50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n50 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n4 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5",
"output": "47"
},
{
"input": "5 4\n300 300 300 300 300\n1 2\n2 3\n3 4\n4 5",
"output": "300"
},
{
"input": "5 2\n4 4 10 3 3\n1 2\n4 5",
"output": "3"
},
{
"input": "6 1\n10 1 1 2 3 4\n2 3",
"output": "1"
},
{
"input": "10 9\n1 1 1 1 1 1 1 1 1 1\n5 8\n8 6\n1 8\n8 4\n3 7\n1 10\n1 9\n2 5\n6 9",
"output": "1"
},
{
"input": "10 15\n1 1 1 1 2 2 2 2 1 2\n8 5\n9 1\n8 6\n3 5\n2 7\n2 9\n10 3\n3 2\n3 6\n4 2\n5 9\n7 3\n6 7\n5 10\n4 7",
"output": "1"
},
{
"input": "7 6\n1 2 3 4 3 3 3\n5 1\n6 1\n7 1\n1 2\n2 3\n2 4",
"output": "2"
},
{
"input": "2 1\n100000 100000\n1 2",
"output": "100000"
}
] | 218 | 5,632,000 | 0 | 14,187 |
|
28 | DravDe saves the world | [
"geometry",
"math"
] | E. DravDe saves the world | 1 | 256 | How horrible! The empire of galactic chickens tries to conquer a beautiful city "Z", they have built a huge incubator that produces millions of chicken soldiers a day, and fenced it around. The huge incubator looks like a polygon on the plane *Oxy* with *n* vertices. Naturally, DravDe can't keep still, he wants to destroy the chicken empire. For sure, he will start with the incubator.
DravDe is strictly outside the incubator's territory in point *A*(*x**a*,<=*y**a*), and wants to get inside and kill all the chickens working there. But it takes a lot of doing! The problem is that recently DravDe went roller skating and has broken both his legs. He will get to the incubator's territory in his jet airplane LEVAP-41.
LEVAP-41 flies at speed *V*(*x**v*,<=*y**v*,<=*z**v*). DravDe can get on the plane in point *A*, fly for some time, and then air drop himself. DravDe is very heavy, that's why he falls vertically at speed *F**down*, but in each point of his free fall DravDe can open his parachute, and from that moment he starts to fall at the wind speed *U*(*x**u*,<=*y**u*,<=*z**u*) until he lands. Unfortunately, DravDe isn't good at mathematics. Would you help poor world's saviour find such an air dropping plan, that allows him to land on the incubator's territory? If the answer is not unique, DravDe wants to find the plan with the minimum time of his flight on the plane. If the answers are still multiple, he wants to find the one with the minimum time of his free fall before opening his parachute | The first line contains the number *n* (3<=≤<=*n*<=≤<=104) — the amount of vertices of the fence. Then there follow *n* lines containing the coordinates of these vertices (two integer numbers *x**i*,<=*y**i*) in clockwise or counter-clockwise order. It's guaranteed, that the fence does not contain self-intersections.
The following four lines contain coordinates of point *A*(*x**a*,<=*y**a*), speeds *V*(*x**v*,<=*y**v*,<=*z**v*), *F**down* and speed *U*(*x**u*,<=*y**u*,<=*z**u*). All the input numbers are integer. All the coordinates don't exceed 104 in absolute value. It's guaranteed, that *z**v*<=><=0 and *F**down*,<=*z**u*<=<<=0, and point *A* is strictly outside the incubator's territory. | In the first line output two numbers *t*1,<=*t*2 such, that if DravDe air drops at time *t*1 (counting from the beginning of the flight), he lands on the incubator's territory (landing on the border is regarder as landing on the territory). If DravDe doesn't open his parachute, the second number should be equal to the duration of DravDe's falling down. If it's impossible for DravDe to get to the incubator's territory, output -1 -1. If the answer is not unique, output the answer with the minimum *t*1. If the answers are still multiple, output the answer with the minimum *t*2. Your answer must have an absolute or relative error less than 10<=-<=6. | [
"4\n0 0\n1 0\n1 1\n0 1\n0 -1\n1 0 1\n-1\n0 1 -1\n",
"4\n0 0\n0 1\n1 1\n1 0\n0 -1\n-1 -1 1\n-1\n0 1 -1\n",
"4\n0 0\n1 0\n1 1\n0 1\n0 -1\n1 1 1\n-1\n1 1 -1\n"
] | [
"1.00000000 0.00000000\n",
"-1.00000000 -1.00000000\n",
"0.50000000 0.00000000\n"
] | none | [
{
"input": "4\n0 0\n1 0\n1 1\n0 1\n0 -1\n1 0 1\n-1\n0 1 -1",
"output": "1.00000000 0.00000000"
},
{
"input": "4\n0 0\n0 1\n1 1\n1 0\n0 -1\n-1 -1 1\n-1\n0 1 -1",
"output": "-1.00000000 -1.00000000"
},
{
"input": "4\n0 0\n1 0\n1 1\n0 1\n0 -1\n1 1 1\n-1\n1 1 -1",
"output": "0.50000000 0.00000000"
},
{
"input": "3\n-3 4\n5 -1\n-1 0\n-4 3\n4 4 5\n-3\n0 -3 -4",
"output": "0.25000000 0.41666667"
},
{
"input": "4\n-2 1\n3 3\n2 -4\n0 -5\n-4 3\n2 4 4\n-4\n2 5 -4",
"output": "-1.00000000 -1.00000000"
},
{
"input": "5\n10 10\n9 10\n8 9\n9 8\n10 9\n-10 -10\n1 1 1\n-1\n0 1 -1",
"output": "18.00000000 17.00000000"
},
{
"input": "10\n-14 18\n17 -17\n13 -16\n8 -13\n0 -4\n0 -8\n-13 16\n-1 -12\n-8 -9\n-11 -6\n2 17\n-20 3 9\n-8\n-5 14 -2",
"output": "-1.00000000 -1.00000000"
},
{
"input": "10\n-17 -17\n-6 13\n-13 -8\n-12 -9\n-7 -2\n-11 -13\n2 -11\n-7 -14\n6 -14\n8 -15\n15 -11\n5 -4 1\n-12\n10 -15 -11",
"output": "-1.00000000 -1.00000000"
},
{
"input": "10\n-16 -7\n-13 -4\n6 11\n17 9\n12 2\n15 -8\n5 -11\n5 -12\n-13 -8\n-7 -19\n-12 1\n-11 -12 5\n-16\n-15 -1 -20",
"output": "-1.00000000 -1.00000000"
},
{
"input": "10\n-19 -8\n-6 17\n0 18\n-9 -2\n9 7\n3 1\n2 -9\n-11 -9\n6 -12\n-16 -10\n3 13\n14 20 16\n-20\n2 11 -17",
"output": "-1.00000000 -1.00000000"
},
{
"input": "10\n-19 -13\n-19 8\n-2 13\n-7 5\n1 17\n8 -3\n15 -2\n15 -10\n12 -11\n11 -13\n3 -19\n-14 -20 7\n-3\n20 -17 -19",
"output": "-1.00000000 -1.00000000"
},
{
"input": "10\n-9 4\n-9 10\n1 9\n4 8\n-4 3\n4 -1\n-1 -1\n9 -8\n8 -9\n0 -6\n10 7\n3 -4 2\n-10\n-7 0 -10",
"output": "-1.00000000 -1.00000000"
},
{
"input": "10\n-7 9\n-6 10\n6 9\n-3 8\n10 2\n1 1\n3 -2\n2 -6\n3 -8\n-5 -3\n10 5\n-7 5 4\n-5\n5 -5 -2",
"output": "0.76923077 0.61538462"
},
{
"input": "10\n-17 -17\n-6 13\n-13 -8\n-12 -9\n-7 -2\n-11 -13\n2 -11\n-7 -14\n6 -14\n8 -15\n-20 0\n5 -4 1\n-12\n10 -15 -11",
"output": "1.17237399 -0.00000000"
},
{
"input": "10\n-8 3\n2 10\n9 6\n-2 3\n1 1\n8 -3\n-6 2\n10 -6\n9 -7\n-3 -5\n10 10\n-7 5 4\n-5\n5 -5 -2",
"output": "2.50000000 0.68000000"
},
{
"input": "4\n-4 -5\n-4 -3\n-4 -2\n2 -5\n-4 3\n0 -4 3\n-3\n0 4 -3",
"output": "1.25000000 1.25000000"
},
{
"input": "4\n-4 2\n1 -3\n0 -4\n-3 -3\n5 4\n0 0 1\n-5\n-1 -1 -2",
"output": "11.00000000 0.00000000"
},
{
"input": "4\n-5 4\n1 5\n2 1\n0 0\n-3 0\n0 0 1\n-5\n2 0 -3",
"output": "4.50000000 0.00000000"
},
{
"input": "4\n-5 4\n1 5\n2 1\n0 0\n-3 -1\n0 0 1\n-5\n2 0 -3",
"output": "-1.00000000 -1.00000000"
},
{
"input": "4\n0 0\n1 0\n1 1\n0 1\n0 -1\n1 1 1\n-5\n0 0 -2",
"output": "1.00000000 0.00000000"
},
{
"input": "4\n0 0\n1 0\n1 1\n0 1\n0 -1\n1 1 1\n-5\n-1 -1 -2",
"output": "1.00000000 0.20000000"
},
{
"input": "10\n-9 7\n-8 10\n3 10\n0 9\n0 7\n5 1\n8 -3\n7 -4\n4 -7\n-5 -10\n10 1\n-10 20 2\n-2\n-1 -5000 -6",
"output": "0.19984006 0.19504198"
},
{
"input": "10\n-9 7\n-8 10\n3 10\n0 9\n0 7\n5 1\n8 -3\n7 -4\n4 -7\n-5 -10\n10 1\n0 0 2\n-2\n0 0 -6",
"output": "-1.00000000 -1.00000000"
},
{
"input": "4\n-8 -2\n8 -2\n8 -5\n-7 -8\n2 -8\n1 2 6\n-4\n-3 -6 -2",
"output": "1.00000000 1.50000000"
},
{
"input": "4\n0 0\n0 1\n1 1\n1 0\n0 -1\n1 1 1\n-2\n1 1 -1",
"output": "0.50000000 0.00000000"
},
{
"input": "4\n0 0\n0 1\n1 1\n1 0\n0 -1\n1 1 1\n-2\n-1 -1 -2",
"output": "1.00000000 0.50000000"
},
{
"input": "4\n-8 -2\n8 -2\n8 -5\n-7 -8\n2 2\n1 2 6\n-4\n-3 -6 -2",
"output": "0.25000000 0.00000000"
},
{
"input": "4\n-4 2\n-2 2\n3 -1\n2 -2\n-100 0\n3 -1 2\n-3\n2 2 -2",
"output": "23.50000000 7.16666667"
},
{
"input": "10\n-5 -4\n-3 0\n-2 2\n0 4\n-1 2\n2 5\n4 5\n-3 -3\n5 1\n1 -5\n10000 2\n-5 4 4\n-1\n1 -5 -3",
"output": "2379.80952381 3807.09523810"
},
{
"input": "10\n-19 20\n-7 20\n2 8\n-9 3\n-8 -3\n-12 3\n-8 -11\n-16 7\n-14 -6\n-14 -8\n13 -10\n11 20 13\n-20\n5 -12 -16",
"output": "-1.00000000 -1.00000000"
},
{
"input": "10\n-16 19\n8 12\n17 7\n6 5\n13 -9\n1 -4\n-7 -4\n-4 -12\n-3 -18\n-10 -3\n-13 5\n-5 12 17\n-4\n19 2 -5",
"output": "0.01264045 -0.00000000"
},
{
"input": "5\n10000 10000\n9999 10000\n9998 9999\n9999 9998\n10000 9999\n-10000 -10000\n1 1 1\n-1\n0 1 -1",
"output": "19998.00000000 19997.00000000"
},
{
"input": "5\n10000 10000\n9999 10000\n9998 9999\n9999 9998\n10000 9999\n-10000 -10000\n1 1 1\n-1\n0 0 -1",
"output": "19998.50000000 0.00000000"
},
{
"input": "5\n10000 10000\n9999 10000\n9998 9999\n9999 9998\n10000 9999\n-10000 -10000\n10000 10000 10000\n-10000\n0 0 -10000",
"output": "1.99985000 0.00000000"
},
{
"input": "5\n10 10\n9 10\n8 9\n9 8\n10 9\n-10 -10\n10000 10000 10000\n-10000\n0 0 -10000",
"output": "0.00185000 0.00000000"
},
{
"input": "10\n-9 -3\n-7 9\n-7 2\n6 7\n1 -2\n3 -5\n-3 -5\n1 -7\n-7 -4\n-6 -6\n-8 8\n10 3 5\n-6\n-1 -6 -2",
"output": "0.08771930 -0.00000000"
},
{
"input": "10\n-7 -5\n-6 -1\n-3 3\n6 7\n0 0\n9 2\n-2 -3\n4 -3\n0 -5\n-2 -7\n-5 2\n8 3 1\n-7\n-5 4 -6",
"output": "0.21739130 0.03105590"
}
] | 30 | 0 | 0 | 14,207 |
400 | Inna and Huge Candy Matrix | [
"implementation",
"math"
] | null | null | Inna and Dima decided to surprise Sereja. They brought a really huge candy matrix, it's big even for Sereja! Let's number the rows of the giant matrix from 1 to *n* from top to bottom and the columns — from 1 to *m*, from left to right. We'll represent the cell on the intersection of the *i*-th row and *j*-th column as (*i*,<=*j*). Just as is expected, some cells of the giant candy matrix contain candies. Overall the matrix has *p* candies: the *k*-th candy is at cell (*x**k*,<=*y**k*).
The time moved closer to dinner and Inna was already going to eat *p* of her favourite sweets from the matrix, when suddenly Sereja (for the reason he didn't share with anyone) rotated the matrix *x* times clockwise by 90 degrees. Then he performed the horizontal rotate of the matrix *y* times. And then he rotated the matrix *z* times counterclockwise by 90 degrees. The figure below shows how the rotates of the matrix looks like.
Inna got really upset, but Duma suddenly understood two things: the candies didn't get damaged and he remembered which cells contained Inna's favourite sweets before Sereja's strange actions. Help guys to find the new coordinates in the candy matrix after the transformation Sereja made! | The first line of the input contains fix integers *n*, *m*, *x*, *y*, *z*, *p* (1<=≤<=*n*,<=*m*<=≤<=109; 0<=≤<=*x*,<=*y*,<=*z*<=≤<=109; 1<=≤<=*p*<=≤<=105).
Each of the following *p* lines contains two integers *x**k*, *y**k* (1<=≤<=*x**k*<=≤<=*n*; 1<=≤<=*y**k*<=≤<=*m*) — the initial coordinates of the *k*-th candy. Two candies can lie on the same cell. | For each of the *p* candies, print on a single line its space-separated new coordinates. | [
"3 3 3 1 1 9\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n3 3\n"
] | [
"1 3\n1 2\n1 1\n2 3\n2 2\n2 1\n3 3\n3 2\n3 1\n"
] | Just for clarity. Horizontal rotating is like a mirroring of the matrix. For matrix: | [
{
"input": "3 3 3 1 1 9\n1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2\n3 3",
"output": "1 3\n1 2\n1 1\n2 3\n2 2\n2 1\n3 3\n3 2\n3 1"
},
{
"input": "5 5 0 0 0 1\n1 4",
"output": "1 4"
},
{
"input": "14 76 376219315 550904689 16684615 24\n11 21\n1 65\n5 25\n14 63\n11 30\n1 19\n5 7\n9 51\n2 49\n13 75\n9 9\n3 63\n8 49\n5 1\n1 67\n13 31\n9 35\n3 53\n13 73\n5 71\n1 32\n5 49\n1 41\n14 69",
"output": "4 21\n14 65\n10 25\n1 63\n4 30\n14 19\n10 7\n6 51\n13 49\n2 75\n6 9\n12 63\n7 49\n10 1\n14 67\n2 31\n6 35\n12 53\n2 73\n10 71\n14 32\n10 49\n14 41\n1 69"
},
{
"input": "63 67 18046757 61758841 85367218 68\n22 30\n25 40\n56 58\n29 11\n34 63\n28 66\n51 5\n39 64\n1 23\n24 61\n19 47\n10 31\n55 28\n52 26\n38 7\n28 31\n13 27\n37 42\n10 52\n19 33\n7 36\n13 1\n46 40\n21 41\n1 1\n6 35\n10 4\n46 9\n21 57\n1 49\n34 14\n14 35\n43 4\n1 41\n25 22\n18 25\n27 23\n43 17\n34 23\n29 4\n50 40\n43 67\n55 37\n4 60\n35 32\n22 58\n22 12\n9 2\n42 44\n20 57\n5 37\n22 48\n26 8\n33 1\n61 28\n55 18\n21 1\n1 2\n36 29\n45 65\n1 41\n22 46\n25 67\n25 41\n36 42\n8 66\n52 60\n28 50",
"output": "38 42\n28 39\n10 8\n57 35\n5 30\n2 36\n63 13\n4 25\n45 63\n7 40\n21 45\n37 54\n40 9\n42 12\n61 26\n37 36\n41 51\n26 27\n16 54\n35 45\n32 57\n67 51\n28 18\n27 43\n67 63\n33 58\n64 54\n59 18\n11 43\n19 63\n54 30\n33 50\n64 21\n27 63\n46 39\n43 46\n45 37\n51 21\n45 30\n64 35\n28 14\n1 21\n31 9\n8 60\n36 29\n10 42\n56 42\n66 55\n24 22\n11 44\n31 59\n20 42\n60 38\n67 31\n40 3\n50 9\n67 43\n66 63\n39 28\n3 19\n27 63\n22 42\n1 39\n27 39\n26 28\n2 56\n8 12\n18 36"
},
{
"input": "75 18 163006189 147424057 443319537 71\n56 7\n1 5\n17 4\n67 13\n45 1\n55 9\n46 14\n23 10\n10 1\n1 1\n14 9\n18 16\n25 9\n22 4\n73 13\n51 7\n43 13\n59 1\n62 15\n37 6\n43 11\n66 17\n61 13\n45 1\n16 7\n46 7\n25 1\n52 13\n74 7\n16 17\n34 11\n37 16\n24 5\n10 11\n20 5\n74 1\n57 7\n72 10\n21 11\n66 13\n46 1\n46 13\n65 1\n68 11\n14 13\n72 11\n58 1\n16 15\n49 1\n53 10\n30 1\n75 1\n45 4\n42 13\n52 10\n25 1\n31 1\n26 1\n21 7\n27 4\n55 10\n61 1\n37 3\n13 18\n24 1\n11 3\n14 17\n34 5\n49 4\n56 13\n19 11",
"output": "20 7\n75 5\n59 4\n9 13\n31 1\n21 9\n30 14\n53 10\n66 1\n75 1\n62 9\n58 16\n51 9\n54 4\n3 13\n25 7\n33 13\n17 1\n14 15\n39 6\n33 11\n10 17\n15 13\n31 1\n60 7\n30 7\n51 1\n24 13\n2 7\n60 17\n42 11\n39 16\n52 5\n66 11\n56 5\n2 1\n19 7\n4 10\n55 11\n10 13\n30 1\n30 13\n11 1\n8 11\n62 13\n4 11\n18 1\n60 15\n27 1\n23 10\n46 1\n1 1\n31 4\n34 13\n24 10\n51 1\n45 1\n50 1\n55 7\n49 4\n21 10\n15 1\n39 3\n63 18\n52 1\n65 3\n62 17\n42 5\n27 4\n20 13\n57 11"
},
{
"input": "99 65 100328801 11658361 60379320 41\n46 61\n92 23\n46 16\n60 56\n50 42\n24 19\n43 54\n40 1\n41 16\n19 34\n57 59\n84 20\n33 3\n82 59\n74 53\n26 65\n83 30\n76 14\n73 55\n58 33\n97 62\n10 18\n70 1\n56 27\n64 25\n25 57\n28 21\n96 2\n10 41\n99 59\n25 15\n1 3\n46 27\n38 65\n34 25\n64 55\n37 53\n78 43\n70 64\n64 49\n4 12",
"output": "61 46\n23 92\n16 46\n56 60\n42 50\n19 24\n54 43\n1 40\n16 41\n34 19\n59 57\n20 84\n3 33\n59 82\n53 74\n65 26\n30 83\n14 76\n55 73\n33 58\n62 97\n18 10\n1 70\n27 56\n25 64\n57 25\n21 28\n2 96\n41 10\n59 99\n15 25\n3 1\n27 46\n65 38\n25 34\n55 64\n53 37\n43 78\n64 70\n49 64\n12 4"
},
{
"input": "60 1 884622497 447787585 45746569 5\n41 1\n3 1\n57 1\n1 1\n28 1",
"output": "20 1\n58 1\n4 1\n60 1\n33 1"
},
{
"input": "29 9 101222353 522378781 221562741 21\n8 1\n12 8\n21 7\n29 2\n12 3\n1 4\n18 9\n28 6\n2 3\n10 8\n16 4\n3 9\n14 4\n15 3\n16 6\n28 7\n18 1\n12 1\n23 1\n11 1\n18 4",
"output": "22 1\n18 8\n9 7\n1 2\n18 3\n29 4\n12 9\n2 6\n28 3\n20 8\n14 4\n27 9\n16 4\n15 3\n14 6\n2 7\n12 1\n18 1\n7 1\n19 1\n12 4"
},
{
"input": "14 33 331499150 82809609 266661996 75\n9 10\n1 1\n8 8\n13 26\n3 1\n5 1\n8 13\n3 19\n1 13\n1 6\n13 1\n12 19\n5 25\n3 10\n6 19\n6 23\n7 1\n11 7\n11 16\n7 32\n8 30\n1 2\n11 2\n13 25\n8 7\n9 33\n9 1\n1 7\n1 30\n14 32\n9 10\n11 7\n12 5\n11 31\n7 10\n7 21\n9 28\n3 23\n11 31\n9 12\n5 14\n9 7\n10 11\n5 14\n5 14\n4 16\n3 32\n3 16\n13 28\n5 10\n2 8\n4 11\n8 4\n11 15\n1 12\n5 17\n14 10\n13 12\n7 7\n2 32\n3 25\n4 5\n4 31\n10 23\n10 28\n5 8\n5 31\n4 25\n3 25\n13 7\n1 26\n6 4\n9 33\n5 4\n1 14",
"output": "6 10\n14 1\n7 8\n2 26\n12 1\n10 1\n7 13\n12 19\n14 13\n14 6\n2 1\n3 19\n10 25\n12 10\n9 19\n9 23\n8 1\n4 7\n4 16\n8 32\n7 30\n14 2\n4 2\n2 25\n7 7\n6 33\n6 1\n14 7\n14 30\n1 32\n6 10\n4 7\n3 5\n4 31\n8 10\n8 21\n6 28\n12 23\n4 31\n6 12\n10 14\n6 7\n5 11\n10 14\n10 14\n11 16\n12 32\n12 16\n2 28\n10 10\n13 8\n11 11\n7 4\n4 15\n14 12\n10 17\n1 10\n2 12\n8 7\n13 32\n12 25\n11 5\n11 31\n5 23\n5 28\n10 8\n10 31\n11 25\n12 25\n2 7\n14 26\n9 4\n6 33\n10 4\n14 14"
},
{
"input": "26 89 146819986 242756320 184308201 43\n20 71\n12 22\n3 73\n9 48\n1 32\n5 20\n1 18\n19 57\n23 77\n1 4\n17 86\n1 13\n16 64\n1 56\n7 63\n18 38\n17 82\n21 43\n5 16\n9 39\n7 23\n5 53\n19 8\n25 10\n11 69\n11 7\n16 47\n25 48\n20 87\n14 16\n1 16\n14 43\n22 43\n11 89\n7 3\n1 57\n5 43\n21 1\n1 21\n3 85\n5 7\n19 16\n7 15",
"output": "71 7\n22 15\n73 24\n48 18\n32 26\n20 22\n18 26\n57 8\n77 4\n4 26\n86 10\n13 26\n64 11\n56 26\n63 20\n38 9\n82 10\n43 6\n16 22\n39 18\n23 20\n53 22\n8 8\n10 2\n69 16\n7 16\n47 11\n48 2\n87 7\n16 13\n16 26\n43 13\n43 5\n89 16\n3 20\n57 26\n43 22\n1 6\n21 26\n85 24\n7 22\n16 8\n15 20"
},
{
"input": "57 62 402127657 5834146 166754152 26\n55 15\n3 10\n10 21\n25 45\n28 50\n54 39\n1 57\n5 11\n13 54\n52 17\n52 9\n28 3\n37 25\n29 15\n55 33\n23 25\n28 1\n46 7\n39 25\n20 43\n33 49\n52 47\n22 11\n37 37\n52 48\n25 53",
"output": "15 3\n10 55\n21 48\n45 33\n50 30\n39 4\n57 57\n11 53\n54 45\n17 6\n9 6\n3 30\n25 21\n15 29\n33 3\n25 35\n1 30\n7 12\n25 19\n43 38\n49 25\n47 6\n11 36\n37 21\n48 6\n53 33"
},
{
"input": "83 53 263444877 330109611 453128994 25\n47 7\n40 13\n47 53\n23 37\n57 23\n4 38\n39 25\n42 41\n61 23\n74 6\n48 5\n56 53\n48 37\n13 37\n34 32\n49 4\n43 32\n14 1\n75 15\n59 18\n25 14\n46 23\n47 48\n72 3\n55 17",
"output": "47 37\n41 44\n1 37\n17 61\n31 27\n16 80\n29 45\n13 42\n31 23\n48 10\n49 36\n1 28\n17 36\n17 71\n22 50\n50 35\n22 41\n53 70\n39 9\n36 25\n40 59\n31 38\n6 37\n51 12\n37 29"
},
{
"input": "65 66 68528825 50348481 104442753 7\n1 49\n54 47\n16 37\n1 34\n51 29\n36 17\n11 16",
"output": "65 49\n12 47\n50 37\n65 34\n15 29\n30 17\n55 16"
},
{
"input": "63 5 311153546 666957619 681867949 3\n14 3\n22 1\n14 2",
"output": "3 50\n5 42\n4 50"
},
{
"input": "1 9 549924215 115901887 855235569 1\n1 6",
"output": "1 4"
},
{
"input": "85 26 48272945 423830401 423026164 3\n35 1\n50 17\n55 2",
"output": "1 35\n17 50\n2 55"
},
{
"input": "67 61 443905131 226973811 158369983 1\n52 51",
"output": "16 51"
},
{
"input": "1 13 348638338 31146449 81215464 3\n1 4\n1 10\n1 6",
"output": "1 4\n1 10\n1 6"
},
{
"input": "68 45 637151929 93583345 392834373 10\n52 11\n28 1\n67 21\n33 29\n43 28\n30 17\n39 30\n52 37\n11 7\n11 26",
"output": "17 11\n41 1\n2 21\n36 29\n26 28\n39 17\n30 30\n17 37\n58 7\n58 26"
},
{
"input": "25 45 20761261 857816695 7926985 1\n1 26",
"output": "25 26"
},
{
"input": "1 1 0 0 0 2\n1 1\n1 1",
"output": "1 1\n1 1"
},
{
"input": "2 2 1 0 0 4\n1 1\n1 2\n2 2\n2 1",
"output": "1 2\n2 2\n2 1\n1 1"
},
{
"input": "2 2 0 1 0 4\n1 1\n1 2\n2 2\n2 1",
"output": "1 2\n1 1\n2 1\n2 2"
},
{
"input": "2 2 0 0 1 4\n1 1\n1 2\n2 2\n2 1",
"output": "2 1\n1 1\n1 2\n2 2"
},
{
"input": "2 1 1 0 0 2\n1 1\n2 1",
"output": "1 2\n1 1"
},
{
"input": "2 1 0 1 0 2\n1 1\n2 1",
"output": "1 1\n2 1"
},
{
"input": "2 1 0 0 1 2\n1 1\n2 1",
"output": "1 1\n1 2"
},
{
"input": "1 1 0 1 0 2\n1 1\n1 1",
"output": "1 1\n1 1"
}
] | 140 | 0 | 0 | 14,254 |
|
57 | Array | [
"combinatorics",
"math"
] | C. Array | 2 | 256 | Chris the Rabbit has been interested in arrays ever since he was a child. At the moment he is researching arrays with the length of *n*, containing only integers from 1 to *n*. He is not good at math, that's why some simple things drive him crazy. For example, yesterday he grew keen on counting how many different beautiful arrays there are. Chris thinks that an array is beautiful if it meets one of the two conditions:
- each elements, starting from the second one, is no more than the preceding one - each element, starting from the second one, is no less than the preceding one
Having got absolutely mad at himself and at math, Chris came to Stewie and Brian to ask them for help. However, they only laughed at him and said that the answer is too simple and not interesting. Help Chris the Rabbit to find the answer at last. | The single line contains an integer *n* which is the size of the array (1<=≤<=*n*<=≤<=105). | You must print the answer on a single line. As it can be rather long, you should print it modulo 1000000007. | [
"2\n",
"3\n"
] | [
"4\n",
"17\n"
] | none | [
{
"input": "2",
"output": "4"
},
{
"input": "3",
"output": "17"
},
{
"input": "12",
"output": "2704144"
},
{
"input": "19",
"output": "345263536"
},
{
"input": "20",
"output": "846527841"
},
{
"input": "26",
"output": "529476652"
},
{
"input": "35",
"output": "358906180"
},
{
"input": "38",
"output": "917151454"
},
{
"input": "42",
"output": "769030659"
},
{
"input": "82",
"output": "105516606"
},
{
"input": "388",
"output": "121470312"
},
{
"input": "691",
"output": "66828054"
},
{
"input": "1000",
"output": "72474738"
},
{
"input": "1300",
"output": "13198519"
},
{
"input": "1589",
"output": "910090838"
},
{
"input": "1885",
"output": "80236682"
},
{
"input": "2197",
"output": "649466350"
},
{
"input": "2490",
"output": "150738377"
},
{
"input": "2798",
"output": "671813603"
},
{
"input": "49948",
"output": "188470824"
},
{
"input": "52402",
"output": "68720508"
},
{
"input": "54904",
"output": "917915735"
},
{
"input": "57500",
"output": "540890446"
},
{
"input": "59913",
"output": "836170548"
},
{
"input": "62467",
"output": "407412105"
},
{
"input": "64922",
"output": "124840329"
},
{
"input": "67491",
"output": "448912826"
},
{
"input": "69942",
"output": "474688044"
},
{
"input": "72484",
"output": "895032755"
},
{
"input": "74977",
"output": "502088741"
},
{
"input": "77461",
"output": "228321485"
},
{
"input": "79964",
"output": "729228388"
},
{
"input": "82463",
"output": "466136228"
},
{
"input": "84999",
"output": "200164009"
},
{
"input": "87440",
"output": "926716958"
},
{
"input": "89915",
"output": "457356022"
},
{
"input": "92481",
"output": "287683730"
},
{
"input": "94962",
"output": "44271116"
},
{
"input": "97469",
"output": "568733613"
},
{
"input": "99925",
"output": "414342728"
},
{
"input": "1662",
"output": "487795363"
},
{
"input": "44892",
"output": "657147284"
},
{
"input": "88122",
"output": "891210641"
},
{
"input": "31353",
"output": "990883671"
},
{
"input": "74583",
"output": "385361995"
},
{
"input": "17813",
"output": "54476064"
},
{
"input": "61043",
"output": "75760676"
},
{
"input": "4273",
"output": "154508332"
},
{
"input": "47504",
"output": "469586508"
},
{
"input": "67828",
"output": "564997335"
},
{
"input": "100000",
"output": "879367333"
},
{
"input": "99999",
"output": "690990293"
},
{
"input": "99998",
"output": "37611412"
},
{
"input": "1",
"output": "1"
}
] | 1,838 | 0 | 3.5405 | 14,261 |
491 | Deciphering | [
"flows",
"graph matchings"
] | null | null | One day Maria Ivanovna found a Sasha's piece of paper with a message dedicated to Olya. Maria Ivanovna wants to know what is there in a message, but unfortunately the message is ciphered. Maria Ivanovna knows that her students usually cipher their messages by replacing each letter of an original message by some another letter. Replacement works in such way that same letters are always replaced with some fixed letter, and different letters are always replaced by different letters.
Maria Ivanovna supposed that the message contains answers to the final exam (since its length is equal to the number of final exam questions). On the other hand she knows that Sasha's answer are not necessary correct. There are *K* possible answers for each questions. Of course, Maria Ivanovna knows correct answers.
Maria Ivanovna decided to decipher message in such way that the number of Sasha's correct answers is maximum possible. She is very busy now, so your task is to help her. | First line contains length of both strings *N* (1<=≤<=*N*<=≤<=2<=000<=000) and an integer *K* — number of possible answers for each of the questions (1<=≤<=*K*<=≤<=52). Answers to the questions are denoted as Latin letters abcde...xyzABCDE...XYZ in the order. For example for *K*<==<=6, possible answers are abcdef and for *K*<==<=30 possible answers are abcde...xyzABCD.
Second line contains a ciphered message string consisting of Latin letters.
Third line contains a correct answers string consisting of Latin letters. | In the first line output maximum possible number of correct Sasha's answers.
In the second line output cipher rule as the string of length *K* where for each letter from the students' cipher (starting from 'a' as mentioned above) there is specified which answer does it correspond to.
If there are several ways to produce maximum answer, output any of them. | [
"10 2\naaabbbaaab\nbbbbabbbbb\n",
"10 2\naaaaaaabbb\nbbbbaaabbb\n",
"9 4\ndacbdacbd\nacbdacbda\n"
] | [
"7\nba\n",
"6\nab\n",
"9\ncdba\n"
] | none | [] | 30 | 0 | 0 | 14,296 |
|
158 | Cd and pwd commands | [
"*special",
"data structures",
"implementation"
] | null | null | Vasya is writing an operating system shell, and it should have commands for working with directories. To begin with, he decided to go with just two commands: cd (change the current directory) and pwd (display the current directory).
Directories in Vasya's operating system form a traditional hierarchical tree structure. There is a single root directory, denoted by the slash character "/". Every other directory has a name — a non-empty string consisting of lowercase Latin letters. Each directory (except for the root) has a parent directory — the one that contains the given directory. It is denoted as "..".
The command cd takes a single parameter, which is a path in the file system. The command changes the current directory to the directory specified by the path. The path consists of the names of directories separated by slashes. The name of the directory can be "..", which means a step up to the parent directory. «..» can be used in any place of the path, maybe several times. If the path begins with a slash, it is considered to be an absolute path, that is, the directory changes to the specified one, starting from the root. If the parameter begins with a directory name (or ".."), it is considered to be a relative path, that is, the directory changes to the specified directory, starting from the current one.
The command pwd should display the absolute path to the current directory. This path must not contain "..".
Initially, the current directory is the root. All directories mentioned explicitly or passed indirectly within any command cd are considered to exist. It is guaranteed that there is no attempt of transition to the parent directory of the root directory. | The first line of the input data contains the single integer *n* (1<=≤<=*n*<=≤<=50) — the number of commands.
Then follow *n* lines, each contains one command. Each of these lines contains either command pwd, or command cd, followed by a space-separated non-empty parameter.
The command parameter cd only contains lower case Latin letters, slashes and dots, two slashes cannot go consecutively, dots occur only as the name of a parent pseudo-directory. The command parameter cd does not end with a slash, except when it is the only symbol that points to the root directory. The command parameter has a length from 1 to 200 characters, inclusive.
Directories in the file system can have the same names. | For each command pwd you should print the full absolute path of the given directory, ending with a slash. It should start with a slash and contain the list of slash-separated directories in the order of being nested from the root to the current folder. It should contain no dots. | [
"7\npwd\ncd /home/vasya\npwd\ncd ..\npwd\ncd vasya/../petya\npwd\n",
"4\ncd /a/b\npwd\ncd ../a/b\npwd\n"
] | [
"/\n/home/vasya/\n/home/\n/home/petya/\n",
"/a/b/\n/a/a/b/\n"
] | none | [
{
"input": "7\npwd\ncd /home/vasya\npwd\ncd ..\npwd\ncd vasya/../petya\npwd",
"output": "/\n/home/vasya/\n/home/\n/home/petya/"
},
{
"input": "4\ncd /a/b\npwd\ncd ../a/b\npwd",
"output": "/a/b/\n/a/a/b/"
},
{
"input": "1\npwd",
"output": "/"
},
{
"input": "2\ncd /test/../test/../test/../test/../a/b/c/..\npwd",
"output": "/a/b/"
},
{
"input": "9\ncd test\npwd\ncd ..\ncd /test\npwd\ncd ..\npwd\ncd test/test\npwd",
"output": "/test/\n/test/\n/\n/test/test/"
},
{
"input": "6\ncd a/a/b/b\npwd\ncd ../..\npwd\ncd ..\npwd",
"output": "/a/a/b/b/\n/a/a/\n/a/"
},
{
"input": "5\npwd\ncd /xgztbykka\npwd\ncd /gia/kxfls\npwd",
"output": "/\n/xgztbykka/\n/gia/kxfls/"
},
{
"input": "17\npwd\ncd denwxe/../jhj/rxit/ie\npwd\ncd /tmyuylvul/qev/ezqit\npwd\ncd ../gxsfgyuspg/irleht\npwd\ncd wq/pqyz/tjotsmdzja\npwd\ncd ia/hs/../u/nemol/ffhf\npwd\ncd /lrdm/mvwxwb/llib\npwd\ncd /lmhu/wloover/rqd\npwd\ncd lkwabdw/../wrqn/x/../ien\npwd",
"output": "/\n/jhj/rxit/ie/\n/tmyuylvul/qev/ezqit/\n/tmyuylvul/qev/gxsfgyuspg/irleht/\n/tmyuylvul/qev/gxsfgyuspg/irleht/wq/pqyz/tjotsmdzja/\n/tmyuylvul/qev/gxsfgyuspg/irleht/wq/pqyz/tjotsmdzja/ia/u/nemol/ffhf/\n/lrdm/mvwxwb/llib/\n/lmhu/wloover/rqd/\n/lmhu/wloover/rqd/wrqn/ien/"
},
{
"input": "5\ncd /xgztbykka\ncd /gia/kxfls\ncd /kiaxt/hcx\ncd /ufzoiv\npwd",
"output": "/ufzoiv/"
},
{
"input": "17\ncd denwxe/../jhj/rxit/ie\ncd /tmyuylvul/qev/ezqit\ncd ../gxsfgyuspg/irleht\ncd wq/pqyz/tjotsmdzja\ncd ia/hs/../u/nemol/ffhf\ncd /lrdm/mvwxwb/llib\ncd /lmhu/wloover/rqd\ncd lkwabdw/../wrqn/x/../ien\ncd /rqljh/qyovqhiry/q\ncd /d/aargbeotxm/ovv\ncd /jaagwy/../xry/w/zdvx\ncd /nblqgcua/s/s/c/dgg\ncd /jktwitbkgj/ee/../../q\ncd wkx/jyphtd/h/../ygwc\ncd areyd/regf/ogvklan\ncd /wrbi/vbxefrd/jimis\npwd",
"output": "/wrbi/vbxefrd/jimis/"
},
{
"input": "5\npwd\ncd ztb/kag\npwd\npwd\npwd",
"output": "/\n/ztb/kag/\n/ztb/kag/\n/ztb/kag/"
},
{
"input": "17\ncd en/ebhjhjzlrx/pmieg\ncd uylvulohqe/wezq/oarx\npwd\ncd yus/fsi/ehtrs/../vjpq\ncd tjotsmdzja/diand/dqb\ncd emolqs/hff/rdmy/vw\ncd ../llibd/mhuos/oove\ncd /rqdqj/kwabd/nj/qng\npwd\ncd /yie/lrq/hmxq/vqhi\ncd qma/../aargbeotxm/ov\ncd /jaagwy/../xry/w/zdvx\npwd\ncd ../gcuagas/s/c/dggmz\npwd\npwd\ncd bkgjifee/../../../vfwkxjoj",
"output": "/en/ebhjhjzlrx/pmieg/uylvulohqe/wezq/oarx/\n/rqdqj/kwabd/nj/qng/\n/xry/w/zdvx/\n/xry/w/gcuagas/s/c/dggmz/\n/xry/w/gcuagas/s/c/dggmz/"
},
{
"input": "50\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd\npwd",
"output": "/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/\n/"
},
{
"input": "11\npwd\ncd /home/vasya\npwd\ncd ..\npwd\ncd vasya/../../petya\npwd\ncd /a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a\npwd\ncd ..\npwd",
"output": "/\n/home/vasya/\n/home/\n/petya/\n/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/\n/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/a/"
}
] | 92 | 0 | 0 | 14,309 |
|
26 | Parquet | [
"combinatorics",
"constructive algorithms",
"greedy",
"implementation"
] | C. Parquet | 2 | 256 | Once Bob decided to lay a parquet floor in his living room. The living room is of size *n*<=×<=*m* metres. Bob had planks of three types: *a* planks 1<=×<=2 meters, *b* planks 2<=×<=1 meters, and *c* planks 2<=×<=2 meters. Help Bob find out, if it is possible to parquet the living room with such a set of planks, and if it is possible, find one of the possible ways to do so. Bob doesn't have to use all the planks. | The first input line contains 5 space-separated integer numbers *n*, *m*, *a*, *b*, *c* (1<=≤<=*n*,<=*m*<=≤<=100,<=0<=≤<=*a*,<=*b*,<=*c*<=≤<=104), *n* and *m* — the living room dimensions, *a*, *b* and *c* — amount of planks 1<=×<=2, 2<=×<=1 и 2<=×<=2 respectively. It's not allowed to turn the planks. | If it is not possible to parquet the room with such a set of planks, output IMPOSSIBLE. Otherwise output one of the possible ways to parquet the room — output *n* lines with *m* lower-case Latin letters each. Two squares with common sides should contain the same letters, if they belong to one and the same plank, and different letters otherwise. Different planks can be marked with one and the same letter (see examples). If the answer is not unique, output any. | [
"2 6 2 2 1\n",
"1 1 100 100 100\n",
"4 4 10 10 10\n"
] | [
"aabcca\naabdda\n",
"IMPOSSIBLE\n",
"aabb\naabb\nbbaa\nbbaa\n"
] | none | [
{
"input": "2 6 2 2 1",
"output": "aaccab\naaddab"
},
{
"input": "1 1 100 100 100",
"output": "IMPOSSIBLE"
},
{
"input": "4 4 10 10 10",
"output": "aacc\naacc\nccaa\nccaa"
},
{
"input": "2 2 0 0 1",
"output": "aa\naa"
},
{
"input": "2 3 2 1 0",
"output": "aac\nbbc"
},
{
"input": "3 2 1 0 1",
"output": "aa\naa\ncc"
},
{
"input": "7 7 9 7 4",
"output": "IMPOSSIBLE"
},
{
"input": "8 10 2 2 18",
"output": "aaccaaccaa\naaccaaccaa\nccaaccaacc\nccaaccaacc\naaccaaccaa\naaccaaccaa\nccaaccaacd\nccaaccbbcd"
},
{
"input": "29 10 89 28 14",
"output": "aaccaaccaa\naaccaaccaa\nccaaccaacc\nccaaccaacc\naaccaaccaa\naaccaaccbb\nccaaccaacc\nddbbddbbdd\naaccaaccaa\nbbddbbddbb\nccaaccaacc\nddbbddbbdd\naaccaaccaa\nbbddbbddbb\nccaaccaacc\nddbbddbbdd\naaccaaccaa\nbbddbbddbb\nccaaccaacc\nddbbddbbdd\naaccaaccaa\nbbddbbddbb\nccabcdabcd\nddabcdabcd\nabcdabcdab\nabcdabcdab\ncdabcdabcd\ncdabcdabcd\naaccaaccaa"
},
{
"input": "56 59 982 294 188",
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},
{
"input": "80 80 668 62 1235",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaacca..."
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{
"input": "100 100 2208 1898 447",
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},
{
"input": "100 100 2474 270 1128",
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},
{
"input": "100 100 570 808 1811",
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},
{
"input": "99 100 1146 3732 36",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccbbddbbddbbddbbddbbddbbddbbdd\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbb\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nb..."
},
{
"input": "95 100 2574 1056 560",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\na..."
},
{
"input": "97 100 58 172 2310",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\na..."
},
{
"input": "100 99 1896 2634 210",
"output": "aaccaaccaacdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabccaaccaaccaaccaaccaaccaaccaaccaaccaac\naaccaaccaacdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabddbbddbbddbbddbbddbbddbbddbbddbbddbbc\nccaaccaaccabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdaaccaaccaaccaaccaaccaaccaaccaaccaacca\nccaaccaaccabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdbbddbbddbbddbbddbbddbbddbbddbbddbbdda\naaccaaccaacdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdaaccaaccaaccaaccaaccaaccaaccaaccaaccaac\naaccaa..."
},
{
"input": "100 95 1528 812 1205",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacdabcdabcdabcdaaccaaccaaccaaccaaccaaccaaccaac\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacdabcdabcdabcdbbddbbddbbddbbddbbddbbddbbddbbc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccabcdabcdabcdabccaaccaaccaaccaaccaaccaaccaacca\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccabcdabcdabcdabddbbddbbddbbddbbddbbddbbddbbdda\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacdabcdabcdabcdaaccaaccaaccaaccaaccaaccaaccaac\naaccaaccaaccaaccaaccaaccaa..."
},
{
"input": "100 97 1362 760 1364",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccabcdabcdabcdabccaaccaaccaaccaaccaaccaacca\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccabcdabcdabcdabddbbddbbddbbddbbddbbddbbdda\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacdabcdabcdabcdaaccaaccaaccaaccaaccaaccaac\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacdabcdabcdabcdbbddbbddbbddbbddbbddbbddbbc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccabcdabcdabcdabccaaccaaccaaccaaccaaccaacca\naaccaaccaaccaacc..."
},
{
"input": "100 1 0 50 0",
"output": "a\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc"
},
{
"input": "1 100 50 0 0",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc"
},
{
"input": "15 16 14 0 53",
"output": "aaccaaccaaccaacc\naaccaaccaaccaacc\nccaaccaaccaaccaa\nccaaccaaccaaccaa\naaccaaccaaccaacc\naaccaaccaaccaacc\nccaaccaaccaaccaa\nccaaccaaccaaccaa\naaccaaccaaccaacc\naaccaaccaaccaacc\nccaaccaaccaaccaa\nccaaccaaccaaccaa\naaccaaccaaccaacc\naaccaaccaaddbbdd\nccaaccaaccaaccaa"
},
{
"input": "12 13 6 8 32",
"output": "aaccaaccaacca\naaccaaccaacca\nccaaccaaccaac\nccaaccaaccaac\naaccaaccaacda\naaccaaccaacda\nccaaccaaccaac\nccaaccaaccbbc\naaccaaccaacca\naaccaaccaadda\nccaaccaaccaac\nccaaccaaccbbc"
},
{
"input": "10 18 4 2 42",
"output": "aaccaaccaaccaaccaa\naaccaaccaaccaaccaa\nccaaccaaccaaccaacc\nccaaccaaccaaccaacc\naaccaaccaaccaaccaa\naaccaaccaaccaaccaa\nccaaccaaccaaccaacc\nccaaccaaccaaccaacc\naaccaaccaaccaaccab\naaccaaccaaccbbddab"
},
{
"input": "99 99 2797 749 677",
"output": "IMPOSSIBLE"
},
{
"input": "100 100 517 5299 1123",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\na..."
},
{
"input": "100 100 561 6219 7541",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\na..."
},
{
"input": "100 100 1685 8218 5037",
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{
"input": "100 100 2808 9139 2533",
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},
{
"input": "100 100 2499 2499 1",
"output": "IMPOSSIBLE"
},
{
"input": "100 100 2499 2499 0",
"output": "IMPOSSIBLE"
},
{
"input": "100 100 2892 2094 7",
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},
{
"input": "90 100 1488 2992 10",
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},
{
"input": "95 100 2942 1808 0",
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},
{
"input": "99 94 1455 3190 4",
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},
{
"input": "78 99 1912 1937 6",
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},
{
"input": "100 100 2499 2499 2",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbdd\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbb\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nb..."
},
{
"input": "100 100 2498 2498 2",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbdd\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbb\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nb..."
},
{
"input": "100 100 2498 2497 2",
"output": "IMPOSSIBLE"
},
{
"input": "100 100 2497 2498 2",
"output": "IMPOSSIBLE"
},
{
"input": "100 100 2498 2498 1",
"output": "IMPOSSIBLE"
},
{
"input": "100 100 10000 10000 10000",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\na..."
},
{
"input": "100 100 0 0 0",
"output": "IMPOSSIBLE"
},
{
"input": "100 1 50 0 100",
"output": "IMPOSSIBLE"
},
{
"input": "100 1 0 50 100",
"output": "a\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc"
},
{
"input": "100 1 0 49 100",
"output": "IMPOSSIBLE"
},
{
"input": "100 1 0 51 100",
"output": "a\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc\na\na\nc\nc"
},
{
"input": "1 100 50 0 100",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc"
},
{
"input": "1 100 51 0 100",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc"
},
{
"input": "1 100 49 0 100",
"output": "IMPOSSIBLE"
},
{
"input": "1 2 1 0 0",
"output": "aa"
},
{
"input": "1 2 0 1 0",
"output": "IMPOSSIBLE"
},
{
"input": "2 1 0 1 0",
"output": "a\na"
},
{
"input": "2 1 1 0 0",
"output": "IMPOSSIBLE"
},
{
"input": "2 2 1 1 0",
"output": "IMPOSSIBLE"
},
{
"input": "2 2 1 1 1",
"output": "aa\naa"
},
{
"input": "2 2 1 2 0",
"output": "ab\nab"
},
{
"input": "2 2 2 1 0",
"output": "aa\nbb"
},
{
"input": "100 100 68 951 133",
"output": "IMPOSSIBLE"
},
{
"input": "90 95 24 117 628",
"output": "IMPOSSIBLE"
},
{
"input": "80 99 20 39 889",
"output": "IMPOSSIBLE"
},
{
"input": "89 100 448 2510 245",
"output": "IMPOSSIBLE"
},
{
"input": "52 52 74 90 594",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaacca..."
},
{
"input": "52 52 4555 2633 7323",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaccaaccaaccaacca..."
},
{
"input": "52 52 1018 324 5",
"output": "aaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\naaccaaccaaddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbdd\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbb\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbdd\nccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaa\nddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbbddbb\naaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaaccaacc\nbbddbbddbbddbbddbbddbbddb..."
},
{
"input": "52 52 29 17 189",
"output": "IMPOSSIBLE"
}
] | 310 | 1,126,400 | 3.920402 | 14,347 |
0 | none | [
"none"
] | null | null | Olya wants to buy a custom wardrobe. It should have *n* boxes with heights *a*1,<=*a*2,<=...,<=*a**n*, stacked one on another in some order. In other words, we can represent each box as a vertical segment of length *a**i*, and all these segments should form a single segment from 0 to without any overlaps.
Some of the boxes are important (in this case *b**i*<==<=1), others are not (then *b**i*<==<=0). Olya defines the convenience of the wardrobe as the number of important boxes such that their bottom edge is located between the heights *l* and *r*, inclusive.
You are given information about heights of the boxes and their importance. Compute the maximum possible convenience of the wardrobe if you can reorder the boxes arbitrarily. | The first line contains three integers *n*, *l* and *r* (1<=≤<=*n*<=≤<=10<=000, 0<=≤<=*l*<=≤<=*r*<=≤<=10<=000) — the number of boxes, the lowest and the highest heights for a bottom edge of an important box to be counted in convenience.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=10<=000) — the heights of the boxes. It is guaranteed that the sum of height of all boxes (i. e. the height of the wardrobe) does not exceed 10<=000: Olya is not very tall and will not be able to reach any higher.
The second line contains *n* integers *b*1,<=*b*2,<=...,<=*b**n* (0<=≤<=*b**i*<=≤<=1), where *b**i* equals 1 if the *i*-th box is important, and 0 otherwise. | Print a single integer — the maximum possible convenience of the wardrobe. | [
"5 3 6\n3 2 5 1 2\n1 1 0 1 0\n",
"2 2 5\n3 6\n1 1\n"
] | [
"2\n",
"1\n"
] | In the first example you can, for example, first put an unimportant box of height 2, then put an important boxes of sizes 1, 3 and 2, in this order, and then the remaining unimportant boxes. The convenience is equal to 2, because the bottom edges of important boxes of sizes 3 and 2 fall into the range [3, 6].
In the second example you have to put the short box under the tall box. | [] | 46 | 0 | 0 | 14,396 |
|
356 | Xenia and Hamming | [
"implementation",
"math"
] | null | null | Xenia is an amateur programmer. Today on the IT lesson she learned about the Hamming distance.
The Hamming distance between two strings *s*<==<=*s*1*s*2... *s**n* and *t*<==<=*t*1*t*2... *t**n* of equal length *n* is value . Record [*s**i*<=≠<=*t**i*] is the Iverson notation and represents the following: if *s**i*<=≠<=*t**i*, it is one, otherwise — zero.
Now Xenia wants to calculate the Hamming distance between two long strings *a* and *b*. The first string *a* is the concatenation of *n* copies of string *x*, that is, . The second string *b* is the concatenation of *m* copies of string *y*.
Help Xenia, calculate the required Hamming distance, given *n*,<=*x*,<=*m*,<=*y*. | The first line contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=1012). The second line contains a non-empty string *x*. The third line contains a non-empty string *y*. Both strings consist of at most 106 lowercase English letters.
It is guaranteed that strings *a* and *b* that you obtain from the input have the same length. | Print a single integer — the required Hamming distance.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. | [
"100 10\na\naaaaaaaaaa\n",
"1 1\nabacaba\nabzczzz\n",
"2 3\nrzr\naz\n"
] | [
"0\n",
"4\n",
"5\n"
] | In the first test case string *a* is the same as string *b* and equals 100 letters a. As both strings are equal, the Hamming distance between them is zero.
In the second test case strings *a* and *b* differ in their 3-rd, 5-th, 6-th and 7-th characters. Thus, the Hamming distance equals 4.
In the third test case string *a* is rzrrzr and string *b* is azazaz. The strings differ in all characters apart for the second one, the Hamming distance between them equals 5. | [] | 46 | 204,800 | -1 | 14,418 |
|
33 | String Problem | [
"shortest paths"
] | B. String Problem | 2 | 256 | Boy Valera likes strings. And even more he likes them, when they are identical. That's why in his spare time Valera plays the following game. He takes any two strings, consisting of lower case Latin letters, and tries to make them identical. According to the game rules, with each move Valera can change one arbitrary character *A**i* in one of the strings into arbitrary character *B**i*, but he has to pay for every move a particular sum of money, equal to *W**i*. He is allowed to make as many moves as he needs. Since Valera is a very economical boy and never wastes his money, he asked you, an experienced programmer, to help him answer the question: what minimum amount of money should Valera have to get identical strings. | The first input line contains two initial non-empty strings *s* and *t*, consisting of lower case Latin letters. The length of each string doesn't exceed 105. The following line contains integer *n* (0<=≤<=*n*<=≤<=500) — amount of possible changings. Then follow *n* lines, each containing characters *A**i* and *B**i* (lower case Latin letters) and integer *W**i* (0<=≤<=*W**i*<=≤<=100), saying that it's allowed to change character *A**i* into character *B**i* in any of the strings and spend sum of money *W**i*. | If the answer exists, output the answer to the problem, and the resulting string. Otherwise output -1 in the only line. If the answer is not unique, output any. | [
"uayd\nuxxd\n3\na x 8\nx y 13\nd c 3\n",
"a\nb\n3\na b 2\na b 3\nb a 5\n",
"abc\nab\n6\na b 4\na b 7\nb a 8\nc b 11\nc a 3\na c 0\n"
] | [
"21\nuxyd\n",
"2\nb\n",
"-1\n"
] | none | [
{
"input": "uayd\nuxxd\n3\na x 8\nx y 13\nd c 3",
"output": "21\nuxyd"
},
{
"input": "a\nb\n3\na b 2\na b 3\nb a 5",
"output": "2\nb"
},
{
"input": "abc\nab\n6\na b 4\na b 7\nb a 8\nc b 11\nc a 3\na c 0",
"output": "-1"
},
{
"input": "xhtuopq\nrtutbz\n10\nh x 10\nx d 3\nr u 4\nu d 1\nt o 100\no t 7\np e 1\ne f 1\nb f 2\nz q 19",
"output": "-1"
},
{
"input": "abad\nabad\n6\na c 3\nb x 100\nd e 7\nr r 10\no t 17\na a 4",
"output": "0\nabad"
},
{
"input": "bbad\nabxd\n4\nb a 7\na b 10\nx a 0\nd t 19",
"output": "7\nabad"
},
{
"input": "abcd\nacer\n6\nb c 100\nc b 10\nc x 1\ne x 3\nc e 7\nr d 11",
"output": "25\nabxd"
},
{
"input": "abac\ncbad\n7\na c 100\nx y 21\nb i 90\nd e 89\nc z 12\nt r 66\na g 78",
"output": "-1"
},
{
"input": "wye\nupt\n13\nz z 5\ne t 8\nt f 2\nf e 3\np l 16\nl s 6\ns q 13\ny o 4\no q 0\nu w 5\nk m 14\nm i 10\nw u 12",
"output": "49\nwqe"
},
{
"input": "xyz\nopr\n10\nx y 0\ny x 0\ny u 4\nu i 3\ni r 2\nr t 1\no w 6\nw t 9\nz r 3\np y 3",
"output": "31\ntxr"
},
{
"input": "aaaaaaaaaa\naaaaaaaaaa\n50\na a 47\na a 40\na a 22\na a 48\na a 37\na a 26\na a 40\na a 28\na a 8\na a 46\na a 42\na a 37\na a 1\na a 0\na a 16\na a 34\na a 12\na a 50\na a 45\na a 49\na a 12\na a 8\na a 32\na a 17\na a 13\na a 1\na a 1\na a 33\na a 1\na a 15\na a 9\na a 11\na a 31\na a 5\na a 18\na a 13\na a 11\na a 20\na a 14\na a 19\na a 15\na a 50\na a 44\na a 23\na a 25\na a 49\na a 7\na a 8\na a 28\na a 38",
"output": "0\naaaaaaaaaa"
},
{
"input": "srumlvfvdnvbwycrtkwnnmsbotsoaf\nuwizokwweugnbegnhjrfdhsfioufvs\n10\nw o 40\nn d 36\nu w 34\nm o 27\nr a 7\ni o 63\ng g 52\ng k 4\ns d 20\ny c 26",
"output": "-1"
},
{
"input": "habege\necjecg\n0",
"output": "-1"
},
{
"input": "babaafbfde\neccefffbee\n10\nm c 15\ng b 5\nh n 6\nm j 12\nl h 7\nd b 15\nm n 0\na f 11\nk d 1\nb a 10",
"output": "-1"
},
{
"input": "bbabcbcbbbccacaaabbb\nccbbbacbbbbcbbcacbba\n5\ne b 72\na a 92\nc b 57\ne a 94\ne d 62",
"output": "-1"
},
{
"input": "bc\nad\n8\nt y 11\nb c 12\nc x 6\nx y 4\nd x 2\na z 4\nz y 2\ne w 1",
"output": "36\nyx"
}
] | 154 | 2,457,600 | 0 | 14,455 |
490 | Treeland Tour | [
"data structures",
"dfs and similar",
"dp",
"trees"
] | null | null | The "Road Accident" band is planning an unprecedented tour around Treeland. The RA fans are looking forward to the event and making bets on how many concerts their favorite group will have.
Treeland consists of *n* cities, some pairs of cities are connected by bidirectional roads. Overall the country has *n*<=-<=1 roads. We know that it is possible to get to any city from any other one. The cities are numbered by integers from 1 to *n*. For every city we know its value *r**i* — the number of people in it.
We know that the band will travel along some path, having concerts in some cities along the path. The band's path will not pass one city twice, each time they move to the city that hasn't been previously visited. Thus, the musicians will travel along some path (without visiting any city twice) and in some (not necessarily all) cities along the way they will have concerts.
The band plans to gather all the big stadiums and concert halls during the tour, so every time they will perform in a city which population is larger than the population of the previously visited with concert city. In other words, the sequence of population in the cities where the concerts will be held is strictly increasing.
In a recent interview with the leader of the "road accident" band promised to the fans that the band will give concert in the largest possible number of cities! Thus the band will travel along some chain of cities of Treeland and have concerts in some of these cities, so that the population number will increase, and the number of concerts will be the largest possible.
The fans of Treeland are frantically trying to figure out how many concerts the group will have in Treeland. Looks like they can't manage without some help from a real programmer! Help the fans find the sought number of concerts. | The first line of the input contains integer *n* (2<=≤<=*n*<=≤<=6000) — the number of cities in Treeland. The next line contains *n* integers *r*1,<=*r*2,<=...,<=*r**n* (1<=≤<=*r**i*<=≤<=106), where *r**i* is the population of the *i*-th city. The next *n*<=-<=1 lines contain the descriptions of the roads, one road per line. Each road is defined by a pair of integers *a**j*, *b**j* (1<=≤<=*a**j*,<=*b**j*<=≤<=*n*) — the pair of the numbers of the cities that are connected by the *j*-th road. All numbers in the lines are separated by spaces. | Print the number of cities where the "Road Accident" band will have concerts. | [
"6\n1 2 3 4 5 1\n1 2\n2 3\n3 4\n3 5\n3 6\n",
"5\n1 2 3 4 5\n1 2\n1 3\n2 4\n3 5\n"
] | [
"4\n",
"3\n"
] | none | [] | 46 | 0 | 0 | 14,470 |
|
630 | Cracking the Code | [
"implementation",
"math"
] | null | null | The protection of a popular program developed by one of IT City companies is organized the following way. After installation it outputs a random five digit number which should be sent in SMS to a particular phone number. In response an SMS activation code arrives.
A young hacker Vasya disassembled the program and found the algorithm that transforms the shown number into the activation code. Note: it is clear that Vasya is a law-abiding hacker, and made it for a noble purpose — to show the developer the imperfection of their protection.
The found algorithm looks the following way. At first the digits of the number are shuffled in the following order <first digit><third digit><fifth digit><fourth digit><second digit>. For example the shuffle of 12345 should lead to 13542. On the second stage the number is raised to the fifth power. The result of the shuffle and exponentiation of the number 12345 is 455 422 043 125 550 171 232. The answer is the 5 last digits of this result. For the number 12345 the answer should be 71232.
Vasya is going to write a keygen program implementing this algorithm. Can you do the same? | The only line of the input contains a positive integer five digit number for which the activation code should be found. | Output exactly 5 digits without spaces between them — the found activation code of the program. | [
"12345\n"
] | [
"71232"
] | none | [
{
"input": "12345",
"output": "71232"
},
{
"input": "13542",
"output": "84443"
},
{
"input": "71232",
"output": "10151"
},
{
"input": "11111",
"output": "36551"
},
{
"input": "10000",
"output": "00000"
},
{
"input": "99999",
"output": "99999"
},
{
"input": "91537",
"output": "27651"
},
{
"input": "70809",
"output": "00000"
},
{
"input": "41675",
"output": "61851"
},
{
"input": "32036",
"output": "82432"
}
] | 46 | 0 | 3 | 14,476 |
|
799 | Fountains | [
"binary search",
"data structures",
"implementation"
] | null | null | Arkady plays Gardenscapes a lot. Arkady wants to build two new fountains. There are *n* available fountains, for each fountain its beauty and cost are known. There are two types of money in the game: coins and diamonds, so each fountain cost can be either in coins or diamonds. No money changes between the types are allowed.
Help Arkady to find two fountains with maximum total beauty so that he can buy both at the same time. | The first line contains three integers *n*, *c* and *d* (2<=≤<=*n*<=≤<=100<=000, 0<=≤<=*c*,<=*d*<=≤<=100<=000) — the number of fountains, the number of coins and diamonds Arkady has.
The next *n* lines describe fountains. Each of these lines contain two integers *b**i* and *p**i* (1<=≤<=*b**i*,<=*p**i*<=≤<=100<=000) — the beauty and the cost of the *i*-th fountain, and then a letter "C" or "D", describing in which type of money is the cost of fountain *i*: in coins or in diamonds, respectively. | Print the maximum total beauty of exactly two fountains Arkady can build. If he can't build two fountains, print 0. | [
"3 7 6\n10 8 C\n4 3 C\n5 6 D\n",
"2 4 5\n2 5 C\n2 1 D\n",
"3 10 10\n5 5 C\n5 5 C\n10 11 D\n"
] | [
"9\n",
"0\n",
"10\n"
] | In the first example Arkady should build the second fountain with beauty 4, which costs 3 coins. The first fountain he can't build because he don't have enough coins. Also Arkady should build the third fountain with beauty 5 which costs 6 diamonds. Thus the total beauty of built fountains is 9.
In the second example there are two fountains, but Arkady can't build both of them, because he needs 5 coins for the first fountain, and Arkady has only 4 coins. | [
{
"input": "3 7 6\n10 8 C\n4 3 C\n5 6 D",
"output": "9"
},
{
"input": "2 4 5\n2 5 C\n2 1 D",
"output": "0"
},
{
"input": "3 10 10\n5 5 C\n5 5 C\n10 11 D",
"output": "10"
},
{
"input": "6 68 40\n1 18 D\n6 16 D\n11 16 D\n7 23 D\n16 30 D\n2 20 D",
"output": "18"
},
{
"input": "6 4 9\n6 6 D\n1 4 D\n6 7 C\n7 6 D\n5 7 D\n2 5 D",
"output": "3"
},
{
"input": "52 38 22\n9 25 D\n28 29 C\n29 25 D\n4 28 D\n23 29 D\n24 25 D\n17 12 C\n11 19 C\n13 14 C\n12 15 D\n7 25 C\n2 25 C\n6 17 C\n2 20 C\n15 23 D\n8 21 C\n13 15 D\n29 15 C\n25 20 D\n22 20 C\n2 13 D\n13 22 D\n27 20 C\n1 21 D\n22 17 C\n14 21 D\n4 25 D\n5 23 C\n9 21 C\n2 20 C\n14 18 C\n29 24 C\n14 29 D\n9 27 C\n23 21 D\n18 26 D\n7 23 C\n13 25 C\n21 26 C\n30 24 C\n21 24 C\n28 22 C\n8 29 C\n3 12 C\n21 22 D\n22 26 C\n13 17 D\n12 12 D\n11 11 C\n18 24 D\n7 13 D\n3 11 C",
"output": "57"
},
{
"input": "6 68 40\n6 16 D\n11 16 D\n1 18 D\n2 20 D\n7 23 D\n16 30 D",
"output": "18"
},
{
"input": "2 1 1\n1 1 C\n1 1 D",
"output": "2"
},
{
"input": "2 100000 100000\n100000 100000 C\n100000 100000 D",
"output": "200000"
},
{
"input": "4 15 9\n5 10 C\n5 10 D\n6 10 D\n7 5 C",
"output": "12"
}
] | 61 | 7,168,000 | 0 | 14,506 |
|
295 | Yaroslav and Points | [
"data structures"
] | null | null | Yaroslav has *n* points that lie on the *Ox* axis. The coordinate of the first point is *x*1, the coordinate of the second point is *x*2, ..., the coordinate of the *n*-th point is — *x**n*. Now Yaroslav wants to execute *m* queries, each of them is of one of the two following types:
1. Move the *p**j*-th point from position *x**p**j* to position *x**p**j*<=+<=*d**j*. At that, it is guaranteed that after executing such query all coordinates of the points will be distinct. 1. Count the sum of distances between all pairs of points that lie on the segment [*l**j*,<=*r**j*] (*l**j*<=≤<=*r**j*). In other words, you should count the sum of: .
Help Yaroslav. | The first line contains integer *n* — the number of points (1<=≤<=*n*<=≤<=105). The second line contains distinct integers *x*1,<=*x*2,<=...,<=*x**n* — the coordinates of points (|*x**i*|<=≤<=109).
The third line contains integer *m* — the number of queries (1<=≤<=*m*<=≤<=105). The next *m* lines contain the queries. The *j*-th line first contains integer *t**j* (1<=≤<=*t**j*<=≤<=2) — the query type. If *t**j*<==<=1, then it is followed by two integers *p**j* and *d**j* (1<=≤<=*p**j*<=≤<=*n*,<=|*d**j*|<=≤<=1000). If *t**j*<==<=2, then it is followed by two integers *l**j* and *r**j* (<=-<=109<=≤<=*l**j*<=≤<=*r**j*<=≤<=109).
It is guaranteed that at any moment all the points have distinct coordinates. | For each type 2 query print the answer on a single line. Print the answers in the order, in which the queries follow in the input.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams of the %I64d specifier. | [
"8\n36 50 28 -75 40 -60 -95 -48\n20\n2 -61 29\n1 5 -53\n1 1 429\n1 5 130\n2 -101 -71\n2 -69 53\n1 1 404\n1 5 518\n2 -101 53\n2 50 872\n1 1 -207\n2 -99 -40\n1 7 -389\n1 6 -171\n1 2 464\n1 7 -707\n1 1 -730\n1 1 560\n2 635 644\n1 7 -677\n"
] | [
"176\n20\n406\n1046\n1638\n156\n0\n"
] | none | [] | 60 | 0 | 0 | 14,509 |
|
8 | Looking for Order | [
"bitmasks",
"dp"
] | C. Looking for Order | 4 | 512 | Girl Lena likes it when everything is in order, and looks for order everywhere. Once she was getting ready for the University and noticed that the room was in a mess — all the objects from her handbag were thrown about the room. Of course, she wanted to put them back into her handbag. The problem is that the girl cannot carry more than two objects at a time, and cannot move the handbag. Also, if he has taken an object, she cannot put it anywhere except her handbag — her inherent sense of order does not let her do so.
You are given the coordinates of the handbag and the coordinates of the objects in some Сartesian coordinate system. It is known that the girl covers the distance between any two objects in the time equal to the squared length of the segment between the points of the objects. It is also known that initially the coordinates of the girl and the handbag are the same. You are asked to find such an order of actions, that the girl can put all the objects back into her handbag in a minimum time period. | The first line of the input file contains the handbag's coordinates *x**s*,<=*y**s*. The second line contains number *n* (1<=≤<=*n*<=≤<=24) — the amount of objects the girl has. The following *n* lines contain the objects' coordinates. All the coordinates do not exceed 100 in absolute value. All the given positions are different. All the numbers are integer. | In the first line output the only number — the minimum time the girl needs to put the objects into her handbag.
In the second line output the possible optimum way for Lena. Each object in the input is described by its index number (from 1 to *n*), the handbag's point is described by number 0. The path should start and end in the handbag's point. If there are several optimal paths, print any of them. | [
"0 0\n2\n1 1\n-1 1\n",
"1 1\n3\n4 3\n3 4\n0 0\n"
] | [
"8\n0 1 2 0 \n",
"32\n0 1 2 0 3 0 \n"
] | none | [
{
"input": "0 0\n2\n1 1\n-1 1",
"output": "8\n0 1 2 0 "
},
{
"input": "1 1\n3\n4 3\n3 4\n0 0",
"output": "32\n0 1 2 0 3 0 "
},
{
"input": "-3 4\n1\n2 2",
"output": "58\n0 1 0 "
},
{
"input": "7 -7\n2\n3 1\n-3 8",
"output": "490\n0 1 2 0 "
},
{
"input": "3 -9\n3\n0 -9\n-10 -3\n-12 -2",
"output": "502\n0 1 0 2 3 0 "
},
{
"input": "4 -1\n4\n14 -3\n-11 10\n-3 -5\n-8 1",
"output": "922\n0 1 0 2 4 0 3 0 "
},
{
"input": "7 -11\n5\n-1 7\n-7 -11\n12 -4\n8 -6\n-18 -8",
"output": "1764\n0 1 3 0 2 5 0 4 0 "
},
{
"input": "11 3\n6\n-17 -17\n-4 -9\n15 19\n7 4\n13 1\n5 -6",
"output": "2584\n0 1 2 0 3 0 4 6 0 5 0 "
},
{
"input": "-6 4\n7\n-10 -11\n-11 -3\n13 27\n12 -22\n19 -17\n21 -21\n-5 4",
"output": "6178\n0 1 4 0 2 0 3 7 0 5 6 0 "
},
{
"input": "27 -5\n8\n-13 -19\n-20 -8\n11 2\n-23 21\n-28 1\n11 -12\n6 29\n22 -15",
"output": "14062\n0 1 2 0 3 7 0 4 5 0 6 8 0 "
},
{
"input": "31 9\n9\n8 -26\n26 4\n3 2\n24 21\n14 34\n-3 26\n35 -25\n5 20\n-1 8",
"output": "9384\n0 1 7 0 2 0 3 9 0 4 5 0 6 8 0 "
},
{
"input": "-44 47\n24\n96 -18\n-50 86\n84 68\n-25 80\n-11 -15\n-62 0\n-42 50\n-57 11\n-5 27\n-44 67\n-77 -3\n-27 -46\n32 63\n86 13\n-21 -51\n-25 -62\n-14 -2\n-21 86\n-92 -94\n-44 -34\n-74 55\n91 -35\n-10 55\n-34 16",
"output": "191534\n0 1 22 0 2 10 0 3 14 0 4 18 0 5 20 0 6 11 0 7 0 8 24 0 9 17 0 12 15 0 13 23 0 16 19 0 21 0 "
},
{
"input": "5 4\n11\n-26 2\n20 35\n-41 39\n31 -15\n-2 -44\n16 -28\n17 -6\n0 7\n-29 -35\n-17 12\n42 29",
"output": "19400\n0 1 3 0 2 11 0 4 6 0 5 9 0 7 0 8 10 0 "
},
{
"input": "-44 22\n12\n-28 24\n41 -19\n-39 -36\n12 -18\n-31 -24\n-7 29\n45 0\n12 -2\n42 31\n28 -37\n-34 -38\n6 24",
"output": "59712\n0 1 5 0 2 10 0 3 11 0 4 8 0 6 12 0 7 9 0 "
},
{
"input": "40 -36\n13\n3 -31\n28 -43\n45 11\n47 -37\n47 -28\n-30 24\n-46 -33\n-31 46\n-2 -38\n-43 -4\n39 11\n45 -1\n50 38",
"output": "52988\n0 1 9 0 2 0 3 13 0 4 5 0 6 8 0 7 10 0 11 12 0 "
},
{
"input": "-54 2\n14\n-21 -2\n-5 34\n48 -55\n-32 -23\n22 -10\n-33 54\n-16 32\n-53 -17\n10 31\n-47 21\n-52 49\n34 42\n-42 -25\n-32 31",
"output": "55146\n0 1 4 0 2 7 0 3 5 0 6 11 0 8 13 0 9 12 0 10 14 0 "
},
{
"input": "-19 -31\n15\n-31 -59\n60 -34\n-22 -59\n5 44\n26 39\n-39 -23\n-60 -7\n1 2\n-5 -19\n-41 -26\n46 -8\n51 -2\n60 4\n-12 44\n14 49",
"output": "60546\n0 1 3 0 2 11 0 4 14 0 5 15 0 6 0 7 10 0 8 9 0 12 13 0 "
},
{
"input": "-34 19\n16\n-44 24\n30 -42\n46 5\n13 -32\n40 53\n35 49\n-30 7\n-60 -50\n37 46\n-18 -57\n37 -44\n-61 58\n13 -55\n28 22\n-50 -3\n5 52",
"output": "81108\n0 1 12 0 2 11 0 3 14 0 4 13 0 5 9 0 6 16 0 7 15 0 8 10 0 "
},
{
"input": "-64 -6\n17\n-3 -18\n66 -58\n55 34\n-4 -40\n-1 -50\n13 -9\n56 55\n3 42\n-54 -52\n51 -56\n21 -27\n62 -17\n54 -5\n-28 -24\n12 68\n43 -22\n8 -6",
"output": "171198\n0 1 14 0 2 10 0 3 7 0 4 5 0 6 17 0 8 15 0 9 0 11 16 0 12 13 0 "
},
{
"input": "7 -35\n18\n24 -3\n25 -42\n-56 0\n63 -30\n18 -63\n-30 -20\n-53 -47\n-11 -17\n-22 -54\n7 -41\n-32 -3\n-29 15\n-30 -25\n68 15\n-18 70\n-28 19\n-12 69\n44 29",
"output": "70504\n0 1 4 0 2 5 0 3 11 0 6 13 0 7 9 0 8 0 10 0 12 16 0 14 18 0 15 17 0 "
},
{
"input": "-8 47\n19\n47 51\n43 -57\n-76 -26\n-23 51\n19 74\n-36 65\n50 4\n48 8\n14 -67\n23 44\n5 59\n7 -45\n-52 -6\n-2 -33\n34 -72\n-51 -47\n-42 4\n-41 55\n22 9",
"output": "112710\n0 1 10 0 2 15 0 3 16 0 4 0 5 11 0 6 18 0 7 8 0 9 12 0 13 17 0 14 19 0 "
},
{
"input": "44 75\n20\n-19 -33\n-25 -42\n-30 -61\n-21 44\n7 4\n-38 -78\n-14 9\n65 40\n-27 25\n65 -1\n-71 -38\n-52 57\n-41 -50\n-52 40\n40 44\n-19 51\n42 -43\n-79 -69\n26 -69\n-56 44",
"output": "288596\n0 1 19 0 2 13 0 3 6 0 4 16 0 5 7 0 8 15 0 9 14 0 10 17 0 11 18 0 12 20 0 "
},
{
"input": "42 -34\n21\n4 62\n43 73\n29 -26\n68 83\n0 52\n-72 34\n-48 44\n64 41\n83 -12\n-25 52\n42 59\n1 38\n12 -79\n-56 -62\n-8 67\n84 -83\n22 -63\n-11 -56\n71 44\n7 55\n-62 65",
"output": "196482\n0 1 15 0 2 4 0 3 0 5 12 0 6 21 0 7 10 0 8 19 0 9 16 0 11 20 0 13 17 0 14 18 0 "
},
{
"input": "-44 42\n22\n-67 -15\n74 -14\n67 76\n-57 58\n-64 78\n29 33\n-27 27\n-20 -52\n-54 -2\n-29 22\n31 -65\n-76 -76\n-29 -51\n-5 -79\n-55 36\n72 36\n-80 -26\n5 60\n-26 69\n78 42\n-47 -84\n8 83",
"output": "181122\n0 1 17 0 2 16 0 3 20 0 4 5 0 6 18 0 7 10 0 8 13 0 9 15 0 11 14 0 12 21 0 19 22 0 "
},
{
"input": "52 92\n23\n-67 -82\n31 82\n-31 -14\n-1 35\n-31 -49\n-75 -14\n78 -51\n-35 -24\n28 -84\n44 -51\n-37 -9\n-38 -91\n41 57\n-19 35\n14 -88\n-60 -60\n-13 -91\n65 -8\n-30 -46\n72 -44\n74 -5\n-79 31\n-3 84",
"output": "492344\n0 1 12 0 2 23 0 3 11 0 4 14 0 5 16 0 6 22 0 7 20 0 8 19 0 9 10 0 13 0 15 17 0 18 21 0 "
},
{
"input": "-21 -47\n24\n-37 1\n-65 8\n-74 74\n58 -7\n81 -31\n-77 90\n-51 10\n-42 -37\n-14 -17\n-26 -71\n62 45\n56 43\n-75 -73\n-33 68\n39 10\n-65 -93\n61 -93\n30 69\n-28 -53\n5 24\n93 38\n-45 -14\n3 -86\n63 -80",
"output": "204138\n0 1 22 0 2 7 0 3 6 0 4 5 0 8 19 0 9 20 0 10 23 0 11 21 0 12 15 0 13 16 0 14 18 0 17 24 0 "
},
{
"input": "31 16\n21\n-9 24\n-59 9\n-25 51\n62 52\n39 15\n83 -24\n45 -81\n42 -62\n57 -56\n-7 -3\n54 47\n-14 -54\n-14 -34\n-19 -60\n-38 58\n68 -63\n-1 -49\n6 75\n-27 22\n-58 -77\n-10 56",
"output": "121890\n0 1 10 0 2 19 0 3 15 0 4 11 0 5 0 6 16 0 7 9 0 8 17 0 12 13 0 14 20 0 18 21 0 "
},
{
"input": "20 -1\n22\n-51 -31\n-41 24\n-19 46\n70 -54\n60 5\n-41 35\n73 -6\n-31 0\n-29 23\n85 9\n-7 -86\n8 65\n-86 66\n-35 14\n11 19\n-66 -34\n-36 61\n84 -10\n-58 -74\n-11 -67\n79 74\n3 -67",
"output": "135950\n0 1 16 0 2 6 0 3 12 0 4 18 0 5 7 0 8 14 0 9 15 0 10 21 0 11 22 0 13 17 0 19 20 0 "
},
{
"input": "-49 4\n23\n-18 -53\n-42 31\n18 -84\n-20 -70\n-12 74\n-72 81\n12 26\n3 9\n-70 -27\n34 -32\n74 -47\n-19 -35\n-46 -8\n-77 90\n7 -42\n81 25\n84 81\n-53 -49\n20 81\n-39 0\n-70 -44\n-63 77\n-67 -73",
"output": "169524\n0 1 4 0 2 22 0 3 15 0 5 19 0 6 14 0 7 8 0 9 21 0 10 11 0 12 13 0 16 17 0 18 23 0 20 0 "
},
{
"input": "-81 35\n24\n58 27\n92 -93\n-82 63\n-55 80\n20 67\n33 93\n-29 46\n-71 -51\n-19 8\n58 -71\n13 60\n0 -48\n-2 -68\n-56 53\n62 52\n64 32\n-12 -63\n-82 -22\n9 -43\n55 12\n77 -21\n26 -25\n-91 -32\n-66 57",
"output": "337256\n0 1 16 0 2 10 0 3 24 0 4 14 0 5 11 0 6 15 0 7 9 0 8 17 0 12 13 0 18 23 0 19 22 0 20 21 0 "
},
{
"input": "45 79\n24\n-66 22\n10 77\n74 88\n59 1\n-51 -86\n-60 91\n1 -51\n-23 85\n3 96\n38 -4\n-55 43\n9 -68\n-4 83\n75 -13\n64 -74\n28 27\n92 -57\n-20 -64\n30 -44\n-95 67\n13 55\n67 -4\n42 77\n61 87",
"output": "277576\n0 1 11 0 2 9 0 3 24 0 4 16 0 5 18 0 6 20 0 7 12 0 8 13 0 10 19 0 14 22 0 15 17 0 21 23 0 "
},
{
"input": "-61 34\n24\n-57 -46\n-37 -24\n-87 -54\n51 -89\n-90 2\n95 -63\n-24 -84\n-85 38\n-52 -62\n96 4\n89 -22\n-16 -3\n-2 -14\n71 -62\n-51 68\n-83 -24\n15 77\n-61 45\n17 -32\n-68 -87\n-93 -28\n-85 24\n-84 -34\n-4 1",
"output": "262400\n0 1 9 0 2 12 0 3 23 0 4 19 0 5 22 0 6 14 0 7 20 0 8 18 0 10 11 0 13 24 0 15 17 0 16 21 0 "
},
{
"input": "70 90\n24\n-64 -96\n-87 -82\n10 -65\n94 22\n95 60\n-13 54\n-83 -92\n95 -50\n-65 -91\n96 -88\n80 -56\n-31 85\n58 86\n-28 22\n-22 45\n-24 -12\n-62 70\n-2 -77\n-31 -72\n61 37\n67 43\n-5 -30\n-84 -59\n-91 51",
"output": "585696\n0 1 7 0 2 23 0 3 18 0 4 8 0 5 0 6 12 0 9 19 0 10 11 0 13 0 14 15 0 16 22 0 17 24 0 20 21 0 "
},
{
"input": "72 -37\n24\n56 -47\n-37 -20\n76 -46\n-14 11\n-63 -46\n52 74\n-60 -23\n27 8\n-78 -26\n15 -23\n74 -90\n39 -64\n86 53\n77 11\n-47 -44\n-1 -14\n90 56\n76 -88\n-27 51\n-67 -8\n-27 4\n83 -91\n54 68\n56 26",
"output": "224008\n0 1 3 0 2 7 0 4 19 0 5 15 0 6 23 0 8 10 0 9 20 0 11 12 0 13 17 0 14 24 0 16 21 0 18 22 0 "
},
{
"input": "9 -5\n10\n-22 23\n22 -26\n10 -32\n18 -34\n7 -27\n2 -38\n-5 -24\n-38 -15\n21 -32\n-17 37",
"output": "13454\n0 1 10 0 2 9 0 3 4 0 5 6 0 7 8 0 "
}
] | 4,000 | 278,118,400 | 0 | 14,514 |
159 | String Manipulation 1.0 | [
"*special",
"binary search",
"brute force",
"data structures",
"strings"
] | null | null | One popular website developed an unusual username editing procedure. One can change the username only by deleting some characters from it: to change the current name *s*, a user can pick number *p* and character *c* and delete the *p*-th occurrence of character *c* from the name. After the user changed his name, he can't undo the change.
For example, one can change name "arca" by removing the second occurrence of character "a" to get "arc".
Polycarpus learned that some user initially registered under nickname *t*, where *t* is a concatenation of *k* copies of string *s*. Also, Polycarpus knows the sequence of this user's name changes. Help Polycarpus figure out the user's final name. | The first line contains an integer *k* (1<=≤<=*k*<=≤<=2000). The second line contains a non-empty string *s*, consisting of lowercase Latin letters, at most 100 characters long. The third line contains an integer *n* (0<=≤<=*n*<=≤<=20000) — the number of username changes. Each of the next *n* lines contains the actual changes, one per line. The changes are written as "*p**i* *c**i*" (without the quotes), where *p**i* (1<=≤<=*p**i*<=≤<=200000) is the number of occurrences of letter *c**i*, *c**i* is a lowercase Latin letter. It is guaranteed that the operations are correct, that is, the letter to be deleted always exists, and after all operations not all letters are deleted from the name. The letters' occurrences are numbered starting from 1. | Print a single string — the user's final name after all changes are applied to it. | [
"2\nbac\n3\n2 a\n1 b\n2 c\n",
"1\nabacaba\n4\n1 a\n1 a\n1 c\n2 b\n"
] | [
"acb\n",
"baa\n"
] | Let's consider the first sample. Initially we have name "bacbac"; the first operation transforms it into "bacbc", the second one — to "acbc", and finally, the third one transforms it into "acb". | [
{
"input": "2\nbac\n3\n2 a\n1 b\n2 c",
"output": "acb"
},
{
"input": "1\nabacaba\n4\n1 a\n1 a\n1 c\n2 b",
"output": "baa"
},
{
"input": "1\naabbabbb\n7\n2 a\n1 a\n1 a\n2 b\n1 b\n3 b\n1 b",
"output": "b"
},
{
"input": "1\na\n0",
"output": "a"
},
{
"input": "4\ndb\n5\n1 d\n2 d\n2 b\n1 d\n2 b",
"output": "bdb"
},
{
"input": "10\nbabcbcbcba\n40\n24 b\n14 a\n19 b\n25 b\n26 c\n7 c\n5 c\n2 a\n4 c\n7 a\n46 b\n14 a\n28 b\n4 c\n5 a\n10 c\n4 c\n4 b\n12 a\n4 a\n30 b\n4 a\n16 b\n4 c\n4 c\n23 b\n8 c\n20 c\n12 c\n2 a\n9 c\n37 b\n11 c\n27 b\n16 c\n5 b\n6 b\n3 c\n4 b\n16 b",
"output": "babcbcbbbabbbbbbbccbbacbcbabacbbaabcbcbabbcbcbbbcbbcababcbba"
},
{
"input": "10\nbcbccaacab\n40\n37 c\n21 a\n18 a\n5 b\n1 a\n8 c\n9 a\n38 c\n10 b\n12 c\n18 a\n23 a\n20 c\n7 b\n33 c\n4 c\n22 c\n28 c\n9 a\n12 a\n22 a\n1 b\n6 a\n31 c\n19 b\n19 a\n15 a\n6 c\n11 c\n18 b\n19 c\n24 c\n8 a\n16 c\n2 c\n12 b\n8 a\n14 c\n18 b\n19 c",
"output": "cbcaabbccaaabbcccacabbccbbcbccabbcaacbbbcaacbccabbccaabbbcab"
},
{
"input": "10\nccbcabbaca\n40\n2 c\n8 b\n26 b\n12 b\n24 a\n29 a\n20 c\n17 b\n32 c\n9 c\n16 b\n13 b\n19 a\n3 c\n2 b\n18 c\n4 a\n13 c\n8 c\n5 c\n13 a\n19 c\n26 c\n13 c\n6 c\n3 c\n4 a\n5 a\n9 c\n8 b\n9 c\n2 c\n19 a\n5 a\n12 c\n10 c\n2 b\n19 c\n21 a\n16 b",
"output": "cbaaacbbbcabbcacccabbaaabcabcabaacbbacaccbcabaccbcbaacbcabbc"
},
{
"input": "10\nabaabbaaac\n40\n10 b\n24 a\n15 a\n7 b\n22 b\n23 b\n50 a\n43 a\n2 c\n24 b\n9 b\n5 c\n6 c\n18 b\n33 a\n5 c\n2 a\n3 c\n2 b\n27 a\n2 c\n4 a\n1 c\n6 a\n1 b\n12 b\n31 a\n13 b\n35 a\n2 c\n40 a\n24 a\n1 c\n31 a\n17 b\n4 b\n1 c\n12 b\n4 b\n39 a",
"output": "aabaaababaaaaabaaaaaabaaabaabbaabaabaaaaaababaaaabaaaaabbaaa"
},
{
"input": "10\nabbaa\n10\n20 a\n2 b\n25 a\n22 a\n13 a\n5 b\n17 b\n1 a\n16 b\n6 a",
"output": "baaabbaabaaabbaabbaaabbaaabbaabbaabaabaa"
}
] | 3,000 | 11,673,600 | 0 | 14,554 |
|
755 | PolandBall and Many Other Balls | [
"combinatorics",
"divide and conquer",
"dp",
"fft",
"math",
"number theory"
] | null | null | PolandBall is standing in a row with Many Other Balls. More precisely, there are exactly *n* Balls. Balls are proud of their home land — and they want to prove that it's strong.
The Balls decided to start with selecting exactly *m* groups of Balls, each consisting either of single Ball or two neighboring Balls. Each Ball can join no more than one group.
The Balls really want to impress their Enemies. They kindly asked you to calculate number of such divisions for all *m* where 1<=≤<=*m*<=≤<=*k*. Output all these values modulo 998244353, the Enemies will be impressed anyway. | There are exactly two numbers *n* and *k* (1<=≤<=*n*<=≤<=109, 1<=≤<=*k*<=<<=215), denoting the number of Balls and the maximim number of groups, respectively. | You should output a sequence of *k* values. The *i*-th of them should represent the sought number of divisions into exactly *i* groups, according to PolandBall's rules. | [
"3 3\n",
"1 1\n",
"5 10\n"
] | [
"5 5 1 ",
"1 ",
"9 25 25 9 1 0 0 0 0 0 "
] | In the first sample case we can divide Balls into groups as follows:
{1}, {2}, {3}, {12}, {23}.
{12}{3}, {1}{23}, {1}{2}, {1}{3}, {2}{3}.
{1}{2}{3}.
Therefore, output is: 5 5 1. | [] | 46 | 0 | 0 | 14,558 |
|
120 | Three Sons | [
"brute force"
] | null | null | Three sons inherited from their father a rectangular corn fiend divided into *n*<=×<=*m* squares. For each square we know how many tons of corn grows on it. The father, an old farmer did not love all three sons equally, which is why he bequeathed to divide his field into three parts containing *A*, *B* and *C* tons of corn.
The field should be divided by two parallel lines. The lines should be parallel to one side of the field and to each other. The lines should go strictly between the squares of the field. Each resulting part of the field should consist of at least one square.
Your task is to find the number of ways to divide the field as is described above, that is, to mark two lines, dividing the field in three parts so that on one of the resulting parts grew *A* tons of corn, *B* on another one and *C* on the remaining one. | The first line contains space-separated integers *n* and *m* — the sizes of the original (1<=≤<=*n*,<=*m*<=≤<=50,<=*max*(*n*,<=*m*)<=≥<=3). Then the field's description follows: *n* lines, each containing *m* space-separated integers *c**ij*, (0<=≤<=*c**ij*<=≤<=100) — the number of tons of corn each square contains. The last line contains space-separated integers *A*,<=*B*,<=*C* (0<=≤<=*A*,<=*B*,<=*C*<=≤<=106). | Print the answer to the problem: the number of ways to divide the father's field so that one of the resulting parts contained *A* tons of corn, another one contained *B* tons, and the remaining one contained *C* tons. If no such way exists, print 0. | [
"3 3\n1 1 1\n1 1 1\n1 1 1\n3 3 3\n",
"2 5\n1 1 1 1 1\n2 2 2 2 2\n3 6 6\n",
"3 3\n1 2 3\n3 1 2\n2 3 1\n5 6 7\n"
] | [
"2\n",
"3\n",
"0\n"
] | The lines dividing the field can be horizontal or vertical, but they should be parallel to each other. | [
{
"input": "3 3\n1 1 1\n1 1 1\n1 1 1\n3 3 3",
"output": "2"
},
{
"input": "2 5\n1 1 1 1 1\n2 2 2 2 2\n3 6 6",
"output": "3"
},
{
"input": "3 3\n1 2 3\n3 1 2\n2 3 1\n5 6 7",
"output": "0"
},
{
"input": "3 3\n0 0 0\n0 0 1\n1 1 0\n2 1 0",
"output": "1"
},
{
"input": "3 3\n0 0 0\n0 1 0\n0 0 0\n1 0 0",
"output": "2"
},
{
"input": "3 2\n0 0\n0 2\n0 0\n2 0 0",
"output": "1"
},
{
"input": "3 2\n0 1\n2 1\n0 1\n3 1 1",
"output": "1"
},
{
"input": "5 10\n0 1 4 4 4 1 4 0 0 4\n1 1 2 0 4 4 2 2 0 3\n3 2 4 0 3 0 1 3 1 0\n4 1 2 3 0 2 0 2 0 1\n4 4 4 0 2 4 3 1 3 2\n10 78 12",
"output": "2"
},
{
"input": "5 10\n0 0 0 0 0 0 0 0 0 0\n0 2 0 1 0 5 0 3 0 4\n0 0 0 0 0 0 0 0 0 0\n0 2 0 4 0 3 0 3 0 2\n0 0 0 0 0 0 0 0 0 0\n0 15 14",
"output": "5"
},
{
"input": "10 10\n2 0 1 5 5 0 4 1 2 0\n3 5 2 5 4 0 2 3 4 0\n4 0 3 0 5 1 2 3 4 4\n1 3 2 0 5 2 4 3 5 0\n5 0 1 5 1 4 4 2 1 2\n3 2 0 4 0 0 0 1 2 4\n3 3 2 2 5 5 2 0 4 3\n3 0 2 5 4 2 5 3 1 4\n2 3 0 3 1 1 0 0 1 4\n3 2 3 5 3 1 0 3 5 5\n45 124 74",
"output": "3"
},
{
"input": "10 15\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0",
"output": "127"
},
{
"input": "10 15\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0",
"output": "127"
},
{
"input": "10 10\n0 0 0 0 0 0 0 0 0 0\n0 6 0 6 0 1 0 4 0 1\n0 0 0 0 0 0 0 0 0 0\n0 4 0 1 0 3 0 4 0 1\n0 0 0 0 0 0 0 0 0 0\n0 3 0 5 0 1 0 2 0 5\n0 0 0 0 0 0 0 0 0 0\n0 1 0 6 0 3 0 4 0 5\n0 0 0 0 0 0 0 0 0 0\n0 3 0 6 0 2 0 4 0 6\n0 69 18",
"output": "6"
},
{
"input": "10 15\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0\n5 20 10",
"output": "24"
},
{
"input": "10 15\n2 91 9 36 34 23 88 86 19 91 29 41 39 47 9\n66 63 69 60 73 19 93 78 15 38 70 39 36 4 49\n93 4 25 32 31 49 33 76 22 83 60 49 47 27 20\n34 9 29 85 84 59 8 87 92 5 44 4 60 63 74\n92 50 27 78 62 88 2 50 95 29 37 3 42 72 80\n41 72 35 1 35 85 42 64 41 79 58 2 41 4 11\n2 3 19 77 97 52 74 37 16 58 57 44 14 94 41\n5 47 75 72 49 52 41 48 59 56 38 54 81 9 50\n54 6 46 52 39 79 30 52 79 68 76 40 44 38 68\n7 12 11 87 78 23 47 14 27 83 83 14 84 54 69\n289 5446 1371",
"output": "0"
},
{
"input": "30 2\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0\n0 0 0",
"output": "406"
},
{
"input": "30 2\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n0 0\n0 1\n12 2 1",
"output": "24"
},
{
"input": "30 2\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n34 34\n1836 68 136",
"output": "6"
},
{
"input": "40 4\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n0 0 0 0\n0 1 0 1\n34 4 2",
"output": "24"
},
{
"input": "40 4\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0 0\n0 0 0",
"output": "744"
}
] | 186 | 2,457,600 | 3 | 14,608 |
|
923 | Picking Strings | [
"constructive algorithms",
"implementation",
"strings"
] | null | null | Alice has a string consisting of characters 'A', 'B' and 'C'. Bob can use the following transitions on any substring of our string in any order any number of times:
- A BC - B AC - C AB - AAA empty string
Note that a substring is one or more consecutive characters. For given queries, determine whether it is possible to obtain the target string from source. | The first line contains a string *S* (1<=≤<=|*S*|<=≤<=105). The second line contains a string *T* (1<=≤<=|*T*|<=≤<=105), each of these strings consists only of uppercase English letters 'A', 'B' and 'C'.
The third line contains the number of queries *Q* (1<=≤<=*Q*<=≤<=105).
The following *Q* lines describe queries. The *i*-th of these lines contains four space separated integers *a**i*, *b**i*, *c**i*, *d**i*. These represent the *i*-th query: is it possible to create *T*[*c**i*..*d**i*] from *S*[*a**i*..*b**i*] by applying the above transitions finite amount of times?
Here, *U*[*x*..*y*] is a substring of *U* that begins at index *x* (indexed from 1) and ends at index *y*. In particular, *U*[1..|*U*|] is the whole string *U*.
It is guaranteed that 1<=≤<=*a*<=≤<=*b*<=≤<=|*S*| and 1<=≤<=*c*<=≤<=*d*<=≤<=|*T*|. | Print a string of *Q* characters, where the *i*-th character is '1' if the answer to the *i*-th query is positive, and '0' otherwise. | [
"AABCCBAAB\nABCB\n5\n1 3 1 2\n2 2 2 4\n7 9 1 1\n3 4 2 3\n4 5 1 3\n"
] | [
"10011\n"
] | In the first query we can achieve the result, for instance, by using transitions <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/2c164f8b6e335aa51b97bbd019ca0d7326927314.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
The third query asks for changing AAB to A — but in this case we are not able to get rid of the character 'B'. | [
{
"input": "AABCCBAAB\nABCB\n5\n1 3 1 2\n2 2 2 4\n7 9 1 1\n3 4 2 3\n4 5 1 3",
"output": "10011"
},
{
"input": "AAAAAA\nAAAAAA\n30\n3 4 1 2\n3 3 4 4\n5 6 3 4\n3 3 2 3\n6 6 1 5\n2 4 4 6\n1 6 2 5\n6 6 3 4\n3 5 1 4\n4 5 3 6\n2 3 2 4\n3 4 4 4\n6 6 4 6\n3 3 2 5\n1 5 3 3\n4 6 1 2\n6 6 6 6\n3 3 3 4\n6 6 6 6\n5 6 4 4\n6 6 5 5\n2 3 1 4\n3 6 4 5\n3 5 6 6\n4 5 2 6\n5 6 6 6\n1 4 2 5\n4 5 2 5\n4 5 1 3\n2 2 4 6",
"output": "111001000000000010101000001000"
},
{
"input": "A\nA\n1\n1 1 1 1",
"output": "1"
},
{
"input": "CCBACACBCCCBBAAC\nCACCAAABAACBBBBAC\n20\n7 7 2 15\n3 11 14 15\n4 9 6 12\n10 15 13 17\n10 16 5 14\n14 15 12 16\n16 16 16 16\n3 15 9 14\n10 12 8 12\n15 15 9 10\n14 15 8 15\n7 14 17 17\n15 15 17 17\n15 15 5 9\n4 14 12 17\n13 15 8 12\n1 4 2 2\n6 13 17 17\n11 14 5 11\n15 16 2 9",
"output": "00001100101000010000"
},
{
"input": "ABAAAAAA\nABABBAAAAAA\n5\n3 8 4 11\n3 8 3 11\n2 8 2 11\n1 8 1 11\n1 8 2 11",
"output": "00111"
},
{
"input": "ABC\nABC\n9\n1 1 1 1\n1 1 2 2\n1 1 3 3\n2 2 1 1\n2 2 2 2\n2 2 3 3\n3 3 1 1\n3 3 2 2\n3 3 3 3",
"output": "100011011"
},
{
"input": "A\nBB\n1\n1 1 1 2",
"output": "1"
},
{
"input": "BBAACCBACACBCCCBBAAC\nCACCAAABAACBBBBACABC\n1\n3 10 6 13",
"output": "0"
},
{
"input": "AAAAACAAAAAB\nAAAAABAAAAAC\n20\n1 6 10 12\n10 12 7 12\n9 12 8 12\n2 6 8 12\n7 12 2 6\n9 12 7 12\n1 6 10 12\n4 6 3 6\n7 12 7 12\n4 6 5 6\n3 6 12 12\n5 6 8 12\n9 12 1 6\n2 6 3 6\n10 12 2 6\n1 6 12 12\n7 12 3 6\n9 12 3 6\n10 12 10 12\n11 12 11 12",
"output": "11111111111111111111"
},
{
"input": "AAABABACACACAAACAC\nAABCBBACABACBBCBCC\n20\n6 17 17 17\n14 17 13 14\n1 13 7 12\n11 17 5 17\n6 10 16 17\n16 17 16 16\n15 17 17 17\n15 15 7 10\n1 4 10 14\n4 11 2 17\n6 9 1 7\n16 16 11 18\n4 14 6 17\n1 17 6 18\n13 18 15 18\n1 12 5 11\n8 8 12 17\n10 15 3 7\n17 17 9 14\n6 17 6 6",
"output": "00010001011111100110"
},
{
"input": "AAACAABB\nCACBCCBB\n10\n2 2 4 5\n4 4 3 3\n1 4 1 8\n5 5 2 8\n7 7 3 4\n6 6 2 2\n1 7 1 1\n6 7 7 8\n4 6 6 8\n8 8 6 8",
"output": "1111010011"
},
{
"input": "A\nCB\n1\n1 1 1 2",
"output": "1"
},
{
"input": "BCBBC\nABBCB\n5\n2 2 2 4\n3 4 2 4\n1 2 2 2\n2 3 4 5\n5 5 2 4",
"output": "10011"
}
] | 685 | 18,534,400 | 3 | 14,646 |
|
0 | none | [
"none"
] | null | null | Natasha travels around Mars in the Mars rover. But suddenly it broke down, namely — the logical scheme inside it. The scheme is an undirected tree (connected acyclic graph) with a root in the vertex $1$, in which every leaf (excluding root) is an input, and all other vertices are logical elements, including the root, which is output. One bit is fed to each input. One bit is returned at the output.
There are four types of logical elements: [AND](https://en.wikipedia.org/wiki/Logical_conjunction) ($2$ inputs), [OR](https://en.wikipedia.org/wiki/Logical_disjunction) ($2$ inputs), [XOR](https://en.wikipedia.org/wiki/Exclusive_or) ($2$ inputs), [NOT](https://en.wikipedia.org/wiki/Negation) ($1$ input). Logical elements take values from their direct descendants (inputs) and return the result of the function they perform. Natasha knows the logical scheme of the Mars rover, as well as the fact that only one input is broken. In order to fix the Mars rover, she needs to change the value on this input.
For each input, determine what the output will be if Natasha changes this input. | The first line contains a single integer $n$ ($2 \le n \le 10^6$) — the number of vertices in the graph (both inputs and elements).
The $i$-th of the next $n$ lines contains a description of $i$-th vertex: the first word "AND", "OR", "XOR", "NOT" or "IN" (means the input of the scheme) is the vertex type. If this vertex is "IN", then the value of this input follows ($0$ or $1$), otherwise follow the indices of input vertices of this element: "AND", "OR", "XOR" have $2$ inputs, whereas "NOT" has $1$ input. The vertices are numbered from one.
It is guaranteed that input data contains a correct logical scheme with an output produced by the vertex $1$. | Print a string of characters '0' and '1' (without quotes) — answers to the problem for each input in the ascending order of their vertex indices. | [
"10\nAND 9 4\nIN 1\nIN 1\nXOR 6 5\nAND 3 7\nIN 0\nNOT 10\nIN 1\nIN 1\nAND 2 8\n"
] | [
"10110"
] | The original scheme from the example (before the input is changed):
<img class="tex-graphics" src="https://espresso.codeforces.com/4507113582d40356e140857daa04318b91197f46.png" style="max-width: 100.0%;max-height: 100.0%;"/>
Green indicates bits '1', yellow indicates bits '0'.
If Natasha changes the input bit $2$ to $0$, then the output will be $1$.
If Natasha changes the input bit $3$ to $0$, then the output will be $0$.
If Natasha changes the input bit $6$ to $1$, then the output will be $1$.
If Natasha changes the input bit $8$ to $0$, then the output will be $1$.
If Natasha changes the input bit $9$ to $0$, then the output will be $0$. | [
{
"input": "10\nAND 9 4\nIN 1\nIN 1\nXOR 6 5\nAND 3 7\nIN 0\nNOT 10\nIN 1\nIN 1\nAND 2 8",
"output": "10110"
},
{
"input": "3\nAND 2 3\nIN 0\nIN 0",
"output": "00"
},
{
"input": "3\nAND 2 3\nIN 1\nIN 0",
"output": "01"
},
{
"input": "3\nAND 2 3\nIN 0\nIN 1",
"output": "10"
},
{
"input": "3\nAND 2 3\nIN 1\nIN 1",
"output": "00"
},
{
"input": "3\nOR 2 3\nIN 0\nIN 0",
"output": "11"
},
{
"input": "3\nOR 2 3\nIN 1\nIN 0",
"output": "01"
},
{
"input": "3\nOR 2 3\nIN 0\nIN 1",
"output": "10"
},
{
"input": "3\nOR 2 3\nIN 1\nIN 1",
"output": "11"
},
{
"input": "3\nXOR 2 3\nIN 0\nIN 0",
"output": "11"
},
{
"input": "3\nXOR 2 3\nIN 1\nIN 0",
"output": "00"
},
{
"input": "3\nXOR 2 3\nIN 0\nIN 1",
"output": "00"
},
{
"input": "3\nXOR 2 3\nIN 1\nIN 1",
"output": "11"
},
{
"input": "2\nNOT 2\nIN 0",
"output": "0"
},
{
"input": "2\nNOT 2\nIN 1",
"output": "1"
},
{
"input": "20\nOR 17 10\nIN 0\nIN 0\nNOT 6\nOR 18 14\nIN 1\nOR 16 3\nXOR 5 4\nIN 0\nXOR 11 9\nNOT 15\nAND 20 19\nIN 0\nIN 1\nIN 1\nNOT 8\nNOT 12\nIN 1\nAND 13 7\nNOT 2",
"output": "11111111"
},
{
"input": "30\nXOR 4 11\nXOR 6 25\nNOT 29\nNOT 9\nNOT 17\nNOT 26\nNOT 30\nNOT 27\nNOT 14\nIN 1\nNOT 5\nNOT 15\nNOT 22\nIN 0\nNOT 24\nIN 1\nNOT 3\nNOT 19\nNOT 8\nNOT 16\nNOT 23\nNOT 28\nNOT 7\nNOT 2\nNOT 10\nNOT 13\nNOT 12\nNOT 20\nNOT 21\nNOT 18",
"output": "000"
},
{
"input": "40\nOR 9 2\nAND 30 31\nIN 1\nIN 1\nIN 0\nOR 25 21\nIN 1\nXOR 20 10\nAND 24 34\nIN 0\nIN 0\nNOT 16\nAND 14 4\nIN 0\nAND 18 27\nIN 1\nAND 15 22\nOR 26 12\nIN 1\nAND 36 3\nXOR 11 38\nIN 1\nIN 1\nNOT 29\nIN 0\nXOR 32 13\nIN 1\nIN 0\nNOT 8\nIN 1\nXOR 37 39\nXOR 7 23\nIN 1\nXOR 33 5\nIN 0\nOR 40 28\nIN 1\nIN 0\nAND 35 17\nXOR 6 19",
"output": "1111111111111111111"
},
{
"input": "50\nNOT 37\nOR 23 10\nIN 1\nAND 28 48\nIN 0\nIN 0\nIN 0\nAND 39 21\nNOT 6\nNOT 40\nAND 18 36\nIN 0\nIN 1\nOR 33 43\nNOT 27\nNOT 25\nNOT 35\nXOR 16 34\nNOT 22\nIN 1\nAND 4 13\nNOT 46\nIN 1\nNOT 3\nOR 5 49\nXOR 30 15\nOR 41 31\nIN 0\nIN 0\nOR 8 38\nIN 1\nAND 7 20\nNOT 11\nIN 1\nXOR 2 32\nXOR 29 9\nAND 50 44\nIN 1\nIN 0\nOR 42 47\nIN 0\nNOT 14\nIN 1\nNOT 19\nIN 1\nIN 0\nNOT 26\nOR 45 12\nIN 1\nOR 24 17",
"output": "0110111111111111111"
},
{
"input": "60\nAND 20 4\nNOT 42\nAND 48 59\nOR 17 7\nIN 0\nAND 36 37\nIN 1\nIN 0\nIN 1\nNOT 47\nAND 52 49\nOR 44 35\nIN 0\nIN 1\nAND 33 56\nIN 0\nIN 0\nIN 0\nAND 31 41\nOR 15 3\nOR 43 46\nIN 1\nXOR 22 28\nIN 1\nIN 1\nIN 1\nAND 34 21\nIN 1\nIN 1\nIN 0\nXOR 51 23\nXOR 10 54\nOR 57 40\nIN 0\nNOT 18\nNOT 25\nIN 1\nAND 5 50\nIN 0\nAND 60 53\nAND 45 8\nIN 0\nIN 1\nNOT 27\nIN 0\nIN 1\nAND 19 2\nOR 29 32\nAND 58 24\nNOT 16\nXOR 55 11\nIN 0\nNOT 30\nAND 12 38\nAND 14 9\nIN 1\nIN 0\nOR 26 6\nIN 0\nAND 13 39",
"output": "000000000000000000000000011"
},
{
"input": "9\nAND 2 3\nIN 1\nOR 4 5\nIN 0\nAND 6 7\nIN 1\nOR 8 9\nIN 0\nIN 0",
"output": "01011"
}
] | 5,000 | 216,780,800 | 0 | 14,673 |
|
27 | Unordered Subsequence | [
"constructive algorithms",
"greedy"
] | C. Unordered Subsequence | 2 | 256 | The sequence is called ordered if it is non-decreasing or non-increasing. For example, sequnces [3, 1, 1, 0] and [1, 2, 3, 100] are ordered, but the sequence [1, 3, 3, 1] is not. You are given a sequence of numbers. You are to find it's shortest subsequence which is not ordered.
A subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. | The first line of the input contains one integer *n* (1<=≤<=*n*<=≤<=105). The second line contains *n* space-separated integers — the given sequence. All numbers in this sequence do not exceed 106 by absolute value. | If the given sequence does not contain any unordered subsequences, output 0. Otherwise, output the length *k* of the shortest such subsequence. Then output *k* integers from the range [1..*n*] — indexes of the elements of this subsequence. If there are several solutions, output any of them. | [
"5\n67 499 600 42 23\n",
"3\n1 2 3\n",
"3\n2 3 1\n"
] | [
"3\n1 3 5\n",
"0\n",
"3\n1 2 3\n"
] | none | [
{
"input": "3\n3 1 2",
"output": "3\n1 2 3"
},
{
"input": "1\n-895376",
"output": "0"
},
{
"input": "2\n166442 61629",
"output": "0"
},
{
"input": "3\n-771740 -255752 -300809",
"output": "3\n1 2 3"
},
{
"input": "4\n-227347 -573134 -671045 11011",
"output": "3\n2 3 4"
},
{
"input": "5\n834472 -373089 441294 -633071 -957672",
"output": "3\n1 2 3"
},
{
"input": "2\n7 8",
"output": "0"
}
] | 778 | 7,680,000 | 0 | 14,693 |
996 | World Cup | [
"binary search",
"math"
] | null | null | Allen wants to enter a fan zone that occupies a round square and has $n$ entrances.
There already is a queue of $a_i$ people in front of the $i$-th entrance. Each entrance allows one person from its queue to enter the fan zone in one minute.
Allen uses the following strategy to enter the fan zone:
- Initially he stands in the end of the queue in front of the first entrance. - Each minute, if he is not allowed into the fan zone during the minute (meaning he is not the first in the queue), he leaves the current queue and stands in the end of the queue of the next entrance (or the first entrance if he leaves the last entrance).
Determine the entrance through which Allen will finally enter the fan zone. | The first line contains a single integer $n$ ($2 \le n \le 10^5$) — the number of entrances.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^9$) — the number of people in queues. These numbers do not include Allen. | Print a single integer — the number of entrance that Allen will use. | [
"4\n2 3 2 0\n",
"2\n10 10\n",
"6\n5 2 6 5 7 4\n"
] | [
"3\n",
"1\n",
"6\n"
] | In the first example the number of people (not including Allen) changes as follows: $[\textbf{2}, 3, 2, 0] \to [1, \textbf{2}, 1, 0] \to [0, 1, \textbf{0}, 0]$. The number in bold is the queue Alles stands in. We see that he will enter the fan zone through the third entrance.
In the second example the number of people (not including Allen) changes as follows: $[\textbf{10}, 10] \to [9, \textbf{9}] \to [\textbf{8}, 8] \to [7, \textbf{7}] \to [\textbf{6}, 6] \to \\ [5, \textbf{5}] \to [\textbf{4}, 4] \to [3, \textbf{3}] \to [\textbf{2}, 2] \to [1, \textbf{1}] \to [\textbf{0}, 0]$.
In the third example the number of people (not including Allen) changes as follows: $[\textbf{5}, 2, 6, 5, 7, 4] \to [4, \textbf{1}, 5, 4, 6, 3] \to [3, 0, \textbf{4}, 3, 5, 2] \to \\ [2, 0, 3, \textbf{2}, 4, 1] \to [1, 0, 2, 1, \textbf{3}, 0] \to [0, 0, 1, 0, 2, \textbf{0}]$. | [
{
"input": "4\n2 3 2 0",
"output": "3"
},
{
"input": "2\n10 10",
"output": "1"
},
{
"input": "6\n5 2 6 5 7 4",
"output": "6"
},
{
"input": "2\n483544186 940350702",
"output": "1"
},
{
"input": "10\n3 3 3 5 6 9 3 1 7 3",
"output": "7"
},
{
"input": "10\n0 8 45 88 48 68 28 55 17 24",
"output": "1"
},
{
"input": "100\n8 8 9 10 6 8 2 4 2 2 10 6 6 10 10 2 3 5 1 2 10 4 2 0 9 4 9 3 0 6 3 2 3 10 10 6 4 6 4 4 2 5 1 4 1 1 9 8 9 5 3 5 5 4 5 5 6 5 3 3 7 2 0 10 9 7 7 3 5 1 0 9 6 3 1 3 4 4 3 6 3 2 1 4 10 2 3 4 4 3 6 7 6 2 1 7 0 6 8 10",
"output": "7"
},
{
"input": "10\n5 6 7 8 9 10 11 12 13 14",
"output": "1"
},
{
"input": "10\n15 14 13 12 11 10 9 8 7 6",
"output": "9"
},
{
"input": "2\n1000000000 1000000000",
"output": "1"
},
{
"input": "3\n3 3 1",
"output": "3"
},
{
"input": "10\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000",
"output": "1"
},
{
"input": "3\n15 8 9",
"output": "2"
},
{
"input": "3\n5 5 5",
"output": "3"
},
{
"input": "3\n41 5 6",
"output": "2"
},
{
"input": "2\n999999999 1000000000",
"output": "1"
},
{
"input": "2\n0 1",
"output": "1"
},
{
"input": "3\n3 2 3",
"output": "1"
},
{
"input": "3\n8 5 8",
"output": "2"
},
{
"input": "4\n5 2 3 4",
"output": "2"
},
{
"input": "2\n0 0",
"output": "1"
},
{
"input": "2\n3 3",
"output": "2"
},
{
"input": "4\n9 2 4 7",
"output": "2"
},
{
"input": "30\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000",
"output": "11"
},
{
"input": "4\n11 10 12 12",
"output": "1"
},
{
"input": "2\n1 0",
"output": "2"
},
{
"input": "6\n7 2 6 5 7 9",
"output": "2"
},
{
"input": "3\n1000000000 1000000000 1000000000",
"output": "2"
},
{
"input": "2\n999999999 999999699",
"output": "2"
},
{
"input": "5\n5 5 5 5 5",
"output": "1"
},
{
"input": "2\n1 1",
"output": "2"
}
] | 15 | 0 | -1 | 14,700 |
|
63 | Dividing Island | [
"constructive algorithms"
] | D. Dividing Island | 2 | 256 | A revolution took place on the Buka Island. New government replaced the old one. The new government includes *n* parties and each of them is entitled to some part of the island according to their contribution to the revolution. However, they can't divide the island.
The island can be conventionally represented as two rectangles *a*<=×<=*b* and *c*<=×<=*d* unit squares in size correspondingly. The rectangles are located close to each other. At that, one of the sides with the length of *a* and one of the sides with the length of *c* lie on one line. You can see this in more details on the picture.
The *i*-th party is entitled to a part of the island equal to *x**i* unit squares. Every such part should fully cover several squares of the island (it is not allowed to cover the squares partially) and be a connected figure. A "connected figure" presupposes that from any square of this party one can move to any other square of the same party moving through edge-adjacent squares also belonging to that party.
Your task is to divide the island between parties. | The first line contains 5 space-separated integers — *a*, *b*, *c*, *d* and *n* (1<=≤<=*a*,<=*b*,<=*c*,<=*d*<=≤<=50, *b*<=≠<=*d*, 1<=≤<=*n*<=≤<=26). The second line contains *n* space-separated numbers. The *i*-th of them is equal to number *x**i* (1<=≤<=*x**i*<=≤<=*a*<=×<=*b*<=+<=*c*<=×<=*d*). It is guaranteed that . | If dividing the island between parties in the required manner is impossible, print "NO" (without the quotes). Otherwise, print "YES" (also without the quotes) and, starting from the next line, print *max*(*b*,<=*d*) lines each containing *a*<=+<=*c* characters. To mark what square should belong to what party, use lowercase Latin letters. For the party that is first in order in the input data, use "a", for the second one use "b" and so on. Use "." for the squares that belong to the sea. The first symbol of the second line of the output data should correspond to the square that belongs to the rectangle *a*<=×<=*b*. The last symbol of the second line should correspond to the square that belongs to the rectangle *c*<=×<=*d*.
If there are several solutions output any. | [
"3 4 2 2 3\n5 8 3\n",
"3 2 1 4 4\n1 2 3 4\n"
] | [
"YES\naaabb\naabbb\ncbb..\nccb..\n",
"YES\nabbd\ncccd\n...d\n...d\n"
] | none | [
{
"input": "3 4 2 2 3\n5 8 3",
"output": "YES\nbbbbc\nbbbcc\naab..\naaa.."
},
{
"input": "3 2 1 4 4\n1 2 3 4",
"output": "YES\ncccd\nbbad\n...d\n...d"
},
{
"input": "1 2 1 1 1\n3",
"output": "YES\naa\na."
},
{
"input": "1 2 1 3 2\n3 2",
"output": "YES\naa\nab\n.b"
},
{
"input": "3 2 4 4 20\n1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1",
"output": "YES\ncdeefgh\nbbalkji\n...mnop\n...tsrq"
},
{
"input": "5 4 2 3 26\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1",
"output": "YES\npqrstuv\nonmlkxw\nfghijyz\nedcba.."
},
{
"input": "11 5 4 13 5\n18 21 22 23 23",
"output": "YES\nccccccccccccccc\ncccccbbbbbbddcc\nbbbbbbbbbbbdddd\nbbbbaaaaaaadddd\naaaaaaaaaaadddd\n...........dddd\n...........dddd\n...........eeed\n...........eeee\n...........eeee\n...........eeee\n...........eeee\n...........eeee"
},
{
"input": "1 13 1 14 7\n4 5 5 4 4 3 2",
"output": "YES\ncc\ncd\ncd\ncd\nbd\nbe\nbe\nbe\nbe\naf\naf\naf\nag\n.g"
},
{
"input": "15 1 1 25 6\n3 14 7 7 5 4",
"output": "YES\naaabbbbbbbbbbbbb\n...............b\n...............c\n...............c\n...............c\n...............c\n...............c\n...............c\n...............c\n...............d\n...............d\n...............d\n...............d\n...............d\n...............d\n...............d\n...............e\n...............e\n...............e\n...............e\n...............e\n...............f\n...............f\n...............f\n...............f"
},
{
"input": "20 30 40 50 1\n2600",
"output": "YES\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaa..."
},
{
"input": "20 31 40 50 5\n513 536 504 544 523",
"output": "YES\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\nbbbbbbbaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\naaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\naaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\naaaaaaaaaa..."
},
{
"input": "23 30 43 50 8\n336 384 367 354 360 355 360 324",
"output": "YES\nbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccccccccccccc\nbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccccccccccccccccccccccccc\nbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccccccccccccccccccccccccc\nbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccccccccccccccccccccccccc\nbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccccccccccccccccccccccccc\nbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccccccccccccccccccccccccc\nbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccccccccccccccccccccccccc\nbbbbbbbbbbbbbbbbbbbbbbbccccccc..."
},
{
"input": "20 29 40 47 12\n212 216 228 186 198 209 216 182 200 206 211 196",
"output": "YES\ncccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc\nccccccccccccccccccccddddcccccccccccccccccccccccccccccccccccc\nccccccccccccccccccccdddddddddddddddddddddddddddddddddddddddd\nccccccccccccccccccccdddddddddddddddddddddddddddddddddddddddd\nccccccccccccccccccccdddddddddddddddddddddddddddddddddddddddd\nccccccccccccccccccccdddddddddddddddddddddddddddddddddddddddd\nccccccccccccccccccccddddddddddddddddddddddeeeeeeeeeeeeeeeeee\nccccccccccccbbbbbbbbeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee\nbbbbbbbbbb..."
},
{
"input": "40 23 19 30 26\n72 64 64 68 56 61 54 69 51 60 62 60 50 53 67 48 55 50 50 55 49 60 52 50 57 53",
"output": "YES\nooooooooooooooooooooooooooooooopppppppppppppppppppppppppppp\noooooooooooooooooooooooooooooooooooonnnnppppppppppppppppppp\nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnpqqqqqqqqqqqqqqqqqq\nnnnnnnnnnmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmqqqqqqqqqqqqqqqqqqq\nlllllllllllllllllllllmmmmmmmmmmmmmmmmmmmqqqqqqqqqqqqqqqqqqr\nlllllllllllllllllllllllllllllllllllllllkrrrrrrrrrrrrrrrrrrr\nkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkrrrrrrrrrrrrrrrrrrr\nkkkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjssssssssrrrrrrrrrrr\njjjjjjjjjjjjjjjjjj..."
},
{
"input": "50 49 50 50 1\n4950",
"output": "YES\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa..."
},
{
"input": "50 49 50 50 7\n745 704 669 705 711 721 695",
"output": "YES\ndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd\ndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd\ndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd\ndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd\ndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd..."
},
{
"input": "50 49 50 50 13\n354 385 399 383 372 378 367 354 402 408 410 383 355",
"output": "YES\ngggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg\ngggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg\ngggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg\ngggggggggggggggggggggggggggggfffffffffffffffffffffhhhhhhhhhhhhgggggggggggggggggggggggggggggggggggggg\nffffffffffffffffffffffffffffffffffffffffffffffffffhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh..."
},
{
"input": "50 49 50 50 20\n249 253 249 272 268 240 221 224 254 258 231 239 258 251 247 224 256 260 260 236",
"output": "YES\njjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjkkkkkkkkkkkk\njjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk\njjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk\njjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk\niiiiiiiiiiiiiiiiiiiiiiiiiiiiiijjjjjjjjjjjjjjjjjjjjkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk..."
},
{
"input": "50 49 50 50 26\n193 169 198 176 187 193 178 190 164 208 186 167 180 182 202 208 203 196 203 193 197 206 196 204 199 172",
"output": "YES\nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnooooooooooooooooooooooooooooo\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmoooooooooooooooooooooooooooooooooooooooooooooooooo\nlllllllllmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmoooooooooooooooooooooooooooooooooooooooooooooooo..."
},
{
"input": "49 49 50 50 26\n183 226 169 183 172 205 191 183 192 173 179 196 193 173 195 183 208 183 181 187 193 193 183 194 199 184",
"output": "YES\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmlllllllllllllllllllllllllllllllllllllllllllllllnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nlllllllllllllllllllllllllllllllllllllllllllllllllnnnnnnnnnnnnnnnnnooooooooooooooooooooooooooooooooo\nl..."
},
{
"input": "50 49 49 50 26\n185 189 177 176 191 189 174 184 202 200 188 214 185 201 168 188 208 182 199 163 178 197 189 187 182 204",
"output": "YES\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmlllllllllllllllllllnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nllllllllllllllllllllllllllllllllllllllllllllllllllnnnnnnnnnoooooooooooooooooooooooooooooooooooooooo\nl..."
},
{
"input": "49 49 49 50 26\n194 208 183 166 179 190 182 203 200 185 190 199 175 193 193 185 155 205 183 180 194 188 172 180 184 185",
"output": "YES\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnmmmm\nlllllllllllllllllllllllllmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nlllllllllllllllllllllllllllllllllllllllllllllllllnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nlllllllllllllllllllllllllllllllllllllllllllllllllnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nllllll..."
},
{
"input": "50 50 50 49 26\n205 221 199 178 191 202 180 192 185 204 183 194 215 216 185 200 182 170 190 180 176 204 166 164 194 174",
"output": "YES\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmllllllllllllllllllllllllllllllllllnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nllllllllllllllllllllllllllllllllllllllllllllllllllnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn..."
},
{
"input": "49 50 50 49 26\n170 186 183 175 224 172 187 188 207 185 195 205 190 190 196 178 172 179 194 193 189 174 187 166 211 204",
"output": "YES\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmlllllllllllllllllllllllnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nlllllllllllllllllllllllllllllllllllllllllllllllllnnnnnnnooooooooooooooooooooooooooooooooooooooooooo\nl..."
},
{
"input": "50 50 49 49 26\n205 191 198 197 170 184 182 189 178 165 196 198 196 178 183 192 217 186 177 189 189 203 185 193 195 165",
"output": "YES\nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nnmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnoooooooooooooooooooo\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmooooooooooooooooooooooooooooooooooooooooooooooooo\nlllmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmooooooooooooooooooooooooooooooooooooooooooooooooo\nl..."
},
{
"input": "49 50 49 49 26\n171 184 205 192 182 166 170 194 184 196 194 185 165 185 190 210 196 169 195 194 173 186 192 196 185 192",
"output": "YES\nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnnnnnnnoooooooooooooooooooooooo\nmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmooooooooooooooooooooooooooooooooooooooooooooooooo\nllllllllllllllllllmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmooooooooooooooooooooooooooooooooooooooooooooooooo\nllllll..."
},
{
"input": "2 4 4 1 2\n9 3",
"output": "YES\naaabbb\naa....\naa....\naa...."
},
{
"input": "2 5 4 1 2\n9 5",
"output": "YES\nabbbbb\naa....\naa....\naa....\naa...."
},
{
"input": "3 5 2 3 2\n14 7",
"output": "YES\naabbb\naaabb\naaabb\naaa..\naaa.."
},
{
"input": "2 5 3 2 3\n8 7 1",
"output": "YES\nbbbbb\naacbb\naa...\naa...\naa..."
},
{
"input": "3 2 2 4 3\n2 6 6",
"output": "YES\nbbbbb\nbaacc\n...cc\n...cc"
},
{
"input": "2 3 4 7 2\n17 17",
"output": "YES\naaaaaa\naaaaaa\naaaaab\n..bbbb\n..bbbb\n..bbbb\n..bbbb"
},
{
"input": "2 2 1 6 2\n5 5",
"output": "YES\naaa\naab\n..b\n..b\n..b\n..b"
},
{
"input": "3 2 2 4 2\n7 7",
"output": "YES\naaaab\naaabb\n...bb\n...bb"
},
{
"input": "2 5 2 2 3\n9 2 3",
"output": "YES\nabbc\naacc\naa..\naa..\naa.."
},
{
"input": "3 4 1 2 2\n11 3",
"output": "YES\naabb\naaab\naaa.\naaa."
},
{
"input": "1 5 4 1 3\n3 3 3",
"output": "YES\nbbccc\nb....\na....\na....\na...."
},
{
"input": "4 1 1 5 3\n3 3 3",
"output": "YES\naaabb\n....b\n....c\n....c\n....c"
},
{
"input": "3 6 2 3 3\n3 18 3",
"output": "YES\nbbbbb\nbbbcb\nbbbcc\nbbb..\nbbb..\naaa.."
},
{
"input": "1 4 3 3 3\n2 9 2",
"output": "YES\nbbbb\nbbbb\nabcc\na..."
},
{
"input": "50 40 50 30 7\n1000 500 600 300 200 500 400",
"output": "YES\ncccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc\ncccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc\nccccccccccccccccccccccccccccccccccccccccccccccccccdddddddddddddddddddddddddddddddddddddddddddddddddd\nccccccccccccccccccccccccccccccccccccccccccccccccccdddddddddddddddddddddddddddddddddddddddddddddddddd\nccccccccccccccccccccccccccccccccccccccccccccccccccdddddddddddddddddddddddddddddddddddddddddddddddd..."
},
{
"input": "50 50 50 49 1\n4950",
"output": "YES\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa..."
},
{
"input": "50 50 50 49 1\n4950",
"output": "YES\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa..."
},
{
"input": "50 50 49 49 3\n1234 123 3544",
"output": "YES\nccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc\nccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc\nccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc\nccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc\nccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc\nc..."
}
] | 216 | 512,000 | 0 | 14,717 |
42 | Guilty --- to the kitchen! | [
"greedy",
"implementation"
] | A. Guilty — to the kitchen! | 2 | 256 | It's a very unfortunate day for Volodya today. He got bad mark in algebra and was therefore forced to do some work in the kitchen, namely to cook borscht (traditional Russian soup). This should also improve his algebra skills.
According to the borscht recipe it consists of *n* ingredients that have to be mixed in proportion litres (thus, there should be *a*1<=·*x*,<=...,<=*a**n*<=·*x* litres of corresponding ingredients mixed for some non-negative *x*). In the kitchen Volodya found out that he has *b*1,<=...,<=*b**n* litres of these ingredients at his disposal correspondingly. In order to correct his algebra mistakes he ought to cook as much soup as possible in a *V* litres volume pan (which means the amount of soup cooked can be between 0 and *V* litres). What is the volume of borscht Volodya will cook ultimately? | The first line of the input contains two space-separated integers *n* and *V* (1<=≤<=*n*<=≤<=20,<=1<=≤<=*V*<=≤<=10000). The next line contains *n* space-separated integers *a**i* (1<=≤<=*a**i*<=≤<=100). Finally, the last line contains *n* space-separated integers *b**i* (0<=≤<=*b**i*<=≤<=100). | Your program should output just one real number — the volume of soup that Volodya will cook. Your answer must have a relative or absolute error less than 10<=-<=4. | [
"1 100\n1\n40\n",
"2 100\n1 1\n25 30\n",
"2 100\n1 1\n60 60\n"
] | [
"40.0\n",
"50.0\n",
"100.0\n"
] | none | [
{
"input": "1 100\n1\n40",
"output": "40.0"
},
{
"input": "2 100\n1 1\n25 30",
"output": "50.0"
},
{
"input": "2 100\n1 1\n60 60",
"output": "100.0"
},
{
"input": "2 100\n1 1\n50 50",
"output": "100.0"
},
{
"input": "2 100\n1 2\n33 66",
"output": "99.0"
},
{
"input": "3 10000\n1 1 1\n100 0 100",
"output": "0.0"
},
{
"input": "7 5100\n21 93 52 80 5 46 20\n79 37 74 54 22 15 90",
"output": "103.3695652173913"
},
{
"input": "10 2707\n80 91 41 99 99 48 81 25 80 17\n88 79 64 78 4 54 38 92 77 61",
"output": "26.70707070707071"
},
{
"input": "19 8111\n44 75 80 69 90 64 58 8 93 50 44 39 7 25 14 52 32 26 26\n38 57 38 23 73 24 4 49 0 34 96 93 14 26 29 89 54 12 24",
"output": "0.0"
},
{
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"output": "45.40845070422535"
},
{
"input": "4 6054\n72 21 14 49\n43 53 42 55",
"output": "93.16666666666666"
},
{
"input": "6 8692\n20 61 56 4 78 76\n73 83 97 45 16 7",
"output": "27.171052631578945"
},
{
"input": "9 5583\n73 31 18 36 38 99 34 50 69\n48 24 75 78 75 69 13 74 3",
"output": "19.478260869565215"
},
{
"input": "1 5215\n24\n85",
"output": "85.0"
},
{
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"output": "76.70422535211266"
},
{
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"output": "55.83838383838385"
},
{
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"output": "42.205882352941174"
},
{
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"output": "104.46428571428571"
},
{
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"output": "0.0"
},
{
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"output": "209.72093023255815"
},
{
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"output": "38.0"
},
{
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"output": "40.74157303370786"
},
{
"input": "1 1966\n85\n99",
"output": "99.0"
},
{
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"output": "112.64516129032259"
},
{
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"output": "180.22500000000002"
},
{
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"output": "35.0"
},
{
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"output": "135.33333333333334"
},
{
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"output": "107.2258064516129"
},
{
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"output": "46.66666666666667"
},
{
"input": "7 8690\n73 93 32 47 80 82 97\n49 49 90 43 89 43 67",
"output": "264.2926829268293"
},
{
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"output": "175.6451612903226"
},
{
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"output": "36.317460317460316"
},
{
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"output": "113.26881720430106"
},
{
"input": "16 1718\n42 68 96 52 47 31 89 5 87 70 25 69 35 86 86 11\n35 37 51 15 33 94 18 48 91 2 4 89 73 93 47 26",
"output": "25.685714285714283"
},
{
"input": "4 575\n24 23 16 64\n85 100 14 13",
"output": "25.796875"
},
{
"input": "9 423\n28 88 41 71 99 24 35 68 90\n7 76 44 27 64 52 92 81 98",
"output": "136.0"
},
{
"input": "2 1437\n66 58\n44 8",
"output": "17.10344827586207"
},
{
"input": "18 4733\n78 53 33 72 38 76 43 51 94 18 22 21 65 60 5 71 88 40\n5 78 50 43 81 44 10 18 23 51 52 31 10 55 63 46 82 92",
"output": "59.48717948717948"
},
{
"input": "16 7170\n17 1 48 51 28 16 41 14 59 93 25 76 46 69 74 41\n54 53 41 25 50 42 37 20 11 35 90 96 78 3 20 38",
"output": "30.391304347826086"
},
{
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"output": "89.99999999999999"
},
{
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"output": "96.0"
},
{
"input": "14 3615\n81 79 13 94 54 69 92 5 47 98 40 64 44 88\n52 73 7 12 29 40 46 47 60 66 63 68 71 4",
"output": "39.45454545454545"
},
{
"input": "18 6283\n50 78 16 38 44 9 23 54 58 82 59 12 69 1 10 6 77 61\n70 59 12 11 98 55 52 12 69 40 100 47 42 21 48 18 14 22",
"output": "135.8181818181818"
},
{
"input": "9 3269\n79 88 15 74 92 33 68 64 45\n55 84 75 50 68 32 41 82 42",
"output": "336.44117647058823"
},
{
"input": "6 1007\n93 23 35 15 25 6\n58 24 11 99 23 47",
"output": "61.91428571428571"
},
{
"input": "11 710\n2 49 56 33 79 69 64 62 64 9 87\n94 34 90 3 13 67 76 80 69 19 41",
"output": "52.18181818181819"
},
{
"input": "18 9292\n15 97 47 88 15 7 15 86 52 40 16 97 2 80 64 37 88 15\n39 47 94 12 34 17 45 39 98 99 19 8 94 50 87 68 31 6",
"output": "71.01030927835052"
},
{
"input": "11 3753\n78 75 17 65 97 36 79 56 97 62 43\n18 41 17 47 14 40 7 57 58 24 98",
"output": "62.46835443037974"
},
{
"input": "13 1407\n21 67 79 68 44 52 18 40 68 56 69 66 25\n26 39 78 93 1 57 58 5 67 49 96 15 16",
"output": "15.295454545454545"
},
{
"input": "20 1479\n69 30 15 62 81 24 5 16 25 65 47 23 62 51 87 50 6 44 88 61\n57 47 76 68 7 57 44 98 24 44 1 79 67 31 72 83 36 65 83 42",
"output": "19.382978723404253"
},
{
"input": "17 3856\n50 59 100 50 80 77 58 86 95 87 30 41 11 99 33 27 75\n47 47 39 62 58 91 55 18 65 47 8 97 31 80 61 87 66",
"output": "221.4418604651163"
},
{
"input": "9 2382\n84 51 95 66 34 77 96 9 57\n3 94 56 22 61 50 23 83 45",
"output": "20.32142857142857"
},
{
"input": "14 1751\n33 82 63 35 67 78 47 27 43 96 58 95 39 29\n42 7 15 83 95 91 60 3 85 39 7 56 39 4",
"output": "67.60975609756098"
},
{
"input": "6 8371\n34 11 24 95 62 32\n98 50 58 46 49 93",
"output": "124.92631578947369"
},
{
"input": "2 5181\n4 1\n6 33",
"output": "7.5"
},
{
"input": "9 632\n51 64 25 25 60 71 56 3 31\n70 28 76 84 86 33 77 11 69",
"output": "168.875"
},
{
"input": "3 2102\n76 15 85\n25 95 80",
"output": "57.89473684210526"
},
{
"input": "5 5005\n5 53 65 52 99\n21 49 9 3 66",
"output": "15.807692307692308"
},
{
"input": "17 8971\n54 62 7 47 48 70 78 96 91 34 84 23 72 75 72 60 21\n4 26 6 41 28 45 70 61 6 75 74 46 17 46 34 27 10",
"output": "65.53846153846153"
},
{
"input": "15 5527\n22 49 56 95 86 23 15 74 38 65 52 92 88 49 54\n33 61 71 95 69 31 30 0 1 93 66 48 65 92 11",
"output": "0.0"
},
{
"input": "20 3696\n87 22 21 83 95 31 28 96 71 25 56 40 70 79 46 87 19 19 34 25\n70 44 34 11 2 1 59 22 46 28 3 53 52 71 34 47 65 71 76 30",
"output": "21.768421052631577"
},
{
"input": "8 5540\n5 9 88 1 74 52 32 79\n17 48 99 33 68 28 2 58",
"output": "21.25"
},
{
"input": "15 303\n33 15 28 14 97 33 77 69 41 76 54 97 11 1 1\n83 70 63 11 71 10 48 65 5 5 82 2 6 79 19",
"output": "13.340206185567009"
},
{
"input": "10 9401\n4 53 39 66 52 42 65 39 1 76\n9 34 16 56 78 14 43 49 95 42",
"output": "145.66666666666666"
},
{
"input": "2 9083\n77 33\n22 22",
"output": "31.42857142857143"
},
{
"input": "16 8826\n29 21 40 93 48 49 43 96 60 68 66 5 96 49 84 44\n94 1 79 12 76 65 99 53 37 39 3 76 15 81 51 91",
"output": "40.5"
},
{
"input": "4 9426\n95 48 98 92\n65 40 43 90",
"output": "146.1122448979592"
},
{
"input": "13 175\n46 77 14 16 84 80 81 36 71 13 87 69 8\n54 46 69 59 30 72 83 97 83 96 43 94 84",
"output": "175.0"
},
{
"input": "13 5023\n11 30 92 40 26 77 33 94 71 2 70 97 50\n32 46 51 14 63 76 34 19 13 34 40 91 23",
"output": "126.88732394366197"
},
{
"input": "18 9978\n26 3 87 84 97 53 70 97 37 57 78 23 34 40 81 62 21 92\n56 73 0 79 93 14 17 80 0 20 3 81 22 71 7 82 71 81",
"output": "0.0"
},
{
"input": "14 8481\n64 2 90 76 49 30 88 32 98 64 20 85 40 35\n55 84 75 43 36 13 67 75 100 19 22 7 5 58",
"output": "63.65882352941177"
},
{
"input": "2 1674\n77 23\n23 25",
"output": "29.87012987012987"
},
{
"input": "10 2112\n45 11 32 14 82 30 34 11 42 56\n18 9 84 99 82 43 61 84 14 70",
"output": "119.0"
},
{
"input": "6 2006\n62 4 3 71 61 10\n37 45 61 84 24 15",
"output": "83.01639344262294"
},
{
"input": "8 3954\n80 77 64 1 50 21 89 26\n30 82 17 20 67 21 31 99",
"output": "108.375"
},
{
"input": "18 7253\n64 77 92 9 32 66 23 34 10 71 8 7 83 9 52 97 29 65\n46 90 65 43 44 63 7 38 38 20 62 9 53 39 17 13 5 90",
"output": "110.96907216494844"
},
{
"input": "4 4384\n42 41 85 79\n29 67 52 55",
"output": "151.1058823529412"
},
{
"input": "7 529\n77 18 67 64 43 51 30\n35 87 17 52 1 97 84",
"output": "8.139534883720929"
},
{
"input": "16 2915\n39 39 81 44 23 47 43 56 7 38 10 100 5 34 87 14\n10 96 34 20 62 88 46 38 29 35 2 43 26 55 31 63",
"output": "133.4"
},
{
"input": "14 6488\n53 41 36 28 17 15 63 33 75 40 85 88 90 100\n7 35 83 2 48 76 93 2 69 56 59 7 25 24",
"output": "46.30303030303031"
}
] | 0 | 0 | -1 | 14,735 |
954 | Runner's Problem | [
"dp",
"matrices",
"sortings"
] | null | null | You are running through a rectangular field. This field can be represented as a matrix with 3 rows and *m* columns. (*i*,<=*j*) denotes a cell belonging to *i*-th row and *j*-th column.
You start in (2,<=1) and have to end your path in (2,<=*m*). From the cell (*i*,<=*j*) you may advance to:
- (*i*<=-<=1,<=*j*<=+<=1) — only if *i*<=><=1, - (*i*,<=*j*<=+<=1), or - (*i*<=+<=1,<=*j*<=+<=1) — only if *i*<=<<=3.
However, there are *n* obstacles blocking your path. *k*-th obstacle is denoted by three integers *a**k*, *l**k* and *r**k*, and it forbids entering any cell (*a**k*,<=*j*) such that *l**k*<=≤<=*j*<=≤<=*r**k*.
You have to calculate the number of different paths from (2,<=1) to (2,<=*m*), and print it modulo 109<=+<=7. | The first line contains two integers *n* and *m* (1<=≤<=*n*<=≤<=104, 3<=≤<=*m*<=≤<=1018) — the number of obstacles and the number of columns in the matrix, respectively.
Then *n* lines follow, each containing three integers *a**k*, *l**k* and *r**k* (1<=≤<=*a**k*<=≤<=3, 2<=≤<=*l**k*<=≤<=*r**k*<=≤<=*m*<=-<=1) denoting an obstacle blocking every cell (*a**k*,<=*j*) such that *l**k*<=≤<=*j*<=≤<=*r**k*. Some cells may be blocked by multiple obstacles. | Print the number of different paths from (2,<=1) to (2,<=*m*), taken modulo 109<=+<=7. If it is impossible to get from (2,<=1) to (2,<=*m*), then the number of paths is 0. | [
"2 5\n1 3 4\n2 2 3\n"
] | [
"2\n"
] | none | [
{
"input": "2 5\n1 3 4\n2 2 3",
"output": "2"
},
{
"input": "50 100\n3 24 49\n2 10 12\n1 87 92\n2 19 60\n2 53 79\n3 65 82\n3 10 46\n1 46 86\n2 55 84\n1 50 53\n3 80 81\n3 66 70\n2 35 52\n1 63 69\n2 65 87\n3 68 75\n1 33 42\n1 56 90\n3 73 93\n2 20 26\n2 42 80\n2 83 87\n3 99 99\n1 14 79\n2 94 97\n1 66 85\n1 7 73\n1 50 50\n2 16 40\n2 76 94\n1 71 98\n1 99 99\n1 61 87\n3 98 98\n2 11 41\n3 67 78\n1 31 58\n3 81 85\n1 81 94\n3 41 83\n3 46 65\n1 94 94\n3 31 38\n1 19 35\n3 50 54\n3 85 90\n3 47 63\n3 62 87\n1 18 75\n1 30 41",
"output": "0"
},
{
"input": "50 100\n1 71 96\n2 34 52\n2 16 95\n1 54 55\n1 65 85\n1 76 92\n2 19 91\n1 26 43\n2 83 95\n2 70 88\n2 67 88\n1 9 75\n2 4 50\n2 9 11\n1 77 92\n1 28 58\n1 23 72\n1 24 75\n2 12 50\n1 54 55\n2 45 93\n1 88 93\n2 98 99\n1 40 58\n2 40 42\n1 16 61\n2 94 94\n1 82 86\n2 81 85\n2 46 46\n2 88 97\n2 6 86\n1 30 86\n2 87 96\n1 44 50\n2 43 88\n1 29 98\n1 39 76\n1 78 94\n1 6 69\n2 92 95\n1 40 68\n1 97 99\n1 85 85\n1 69 74\n1 23 51\n1 34 66\n2 70 98\n2 94 97\n1 54 73",
"output": "5"
}
] | 62 | 0 | 0 | 14,737 |
|
245 | Queries for Number of Palindromes | [
"dp",
"hashing",
"strings"
] | null | null | You've got a string *s*<==<=*s*1*s*2... *s*|*s*| of length |*s*|, consisting of lowercase English letters. There also are *q* queries, each query is described by two integers *l**i*,<=*r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=|*s*|). The answer to the query is the number of substrings of string *s*[*l**i*... *r**i*], which are palindromes.
String *s*[*l*... *r*]<==<=*s**l**s**l*<=+<=1... *s**r* (1<=≤<=*l*<=≤<=*r*<=≤<=|*s*|) is a substring of string *s*<==<=*s*1*s*2... *s*|*s*|.
String *t* is called a palindrome, if it reads the same from left to right and from right to left. Formally, if *t*<==<=*t*1*t*2... *t*|*t*|<==<=*t*|*t*|*t*|*t*|<=-<=1... *t*1. | The first line contains string *s* (1<=≤<=|*s*|<=≤<=5000). The second line contains a single integer *q* (1<=≤<=*q*<=≤<=106) — the number of queries. Next *q* lines contain the queries. The *i*-th of these lines contains two space-separated integers *l**i*,<=*r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=|*s*|) — the description of the *i*-th query.
It is guaranteed that the given string consists only of lowercase English letters. | Print *q* integers — the answers to the queries. Print the answers in the order, in which the queries are given in the input. Separate the printed numbers by whitespaces. | [
"caaaba\n5\n1 1\n1 4\n2 3\n4 6\n4 5\n"
] | [
"1\n7\n3\n4\n2\n"
] | Consider the fourth query in the first test case. String *s*[4... 6] = «aba». Its palindrome substrings are: «a», «b», «a», «aba». | [
{
"input": "caaaba\n5\n1 1\n1 4\n2 3\n4 6\n4 5",
"output": "1\n7\n3\n4\n2"
},
{
"input": "a\n100\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1",
"output": "1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1"
},
{
"input": "ab\n100\n1 2\n1 2\n1 1\n1 1\n1 1\n1 1\n1 2\n1 2\n1 2\n1 2\n1 2\n1 1\n1 1\n1 1\n1 2\n1 1\n1 2\n1 2\n2 2\n1 1\n1 1\n2 2\n1 1\n1 2\n1 1\n1 2\n1 2\n1 1\n1 1\n1 2\n1 2\n1 1\n2 2\n1 2\n2 2\n2 2\n2 2\n2 2\n2 2\n1 2\n2 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n2 2\n2 2\n1 1\n2 2\n1 1\n1 1\n1 2\n1 1\n2 2\n1 1\n1 2\n1 1\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 1\n1 2\n1 1\n1 2\n1 2\n1 2\n2 2\n1 1\n2 2\n2 2\n2 2\n2 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 1\n2 2\n1 1\n1 2\n2 2\n1 2\n1 1\n2 2\n1 2\n2 2\n2 2\n1 2\n1 1\n1 2\n2 2",
"output": "2\n2\n1\n1\n1\n1\n2\n2\n2\n2\n2\n1\n1\n1\n2\n1\n2\n2\n1\n1\n1\n1\n1\n2\n1\n2\n2\n1\n1\n2\n2\n1\n1\n2\n1\n1\n1\n1\n1\n2\n1\n2\n2\n2\n2\n2\n2\n2\n1\n1\n1\n1\n1\n1\n2\n1\n1\n1\n2\n1\n2\n2\n2\n2\n2\n2\n2\n2\n1\n2\n1\n2\n2\n2\n1\n1\n1\n1\n1\n1\n2\n2\n2\n2\n2\n1\n1\n1\n2\n1\n2\n1\n1\n2\n1\n1\n2\n1\n2\n1"
},
{
"input": "caa\n100\n2 3\n2 3\n1 3\n2 3\n2 2\n2 3\n1 1\n1 3\n1 3\n1 2\n3 3\n1 3\n1 3\n3 3\n1 2\n1 3\n1 3\n2 2\n2 2\n1 2\n1 3\n1 3\n1 3\n1 2\n3 3\n1 1\n2 3\n2 3\n1 2\n2 3\n1 3\n1 2\n1 3\n2 3\n3 3\n1 2\n2 3\n1 2\n1 3\n1 1\n2 2\n2 2\n2 3\n2 2\n2 3\n1 3\n1 1\n1 2\n1 3\n1 3\n2 3\n1 2\n1 3\n1 2\n1 3\n1 2\n1 1\n1 1\n1 2\n2 3\n1 1\n2 3\n3 3\n2 2\n1 2\n1 3\n1 2\n1 2\n1 2\n2 3\n1 2\n1 2\n1 3\n3 3\n1 2\n2 2\n1 2\n2 2\n1 1\n2 3\n1 2\n1 2\n1 2\n1 2\n2 2\n1 1\n1 2\n3 3\n2 3\n1 2\n1 2\n2 3\n1 2\n1 2\n1 3\n2 3\n1 3\n1 1\n2 2\n1 2",
"output": "3\n3\n4\n3\n1\n3\n1\n4\n4\n2\n1\n4\n4\n1\n2\n4\n4\n1\n1\n2\n4\n4\n4\n2\n1\n1\n3\n3\n2\n3\n4\n2\n4\n3\n1\n2\n3\n2\n4\n1\n1\n1\n3\n1\n3\n4\n1\n2\n4\n4\n3\n2\n4\n2\n4\n2\n1\n1\n2\n3\n1\n3\n1\n1\n2\n4\n2\n2\n2\n3\n2\n2\n4\n1\n2\n1\n2\n1\n1\n3\n2\n2\n2\n2\n1\n1\n2\n1\n3\n2\n2\n3\n2\n2\n4\n3\n4\n1\n1\n2"
},
{
"input": "ccca\n100\n2 4\n1 2\n1 1\n2 3\n3 4\n3 4\n2 2\n3 3\n1 2\n1 4\n2 2\n1 3\n1 4\n4 4\n1 2\n2 3\n3 4\n1 3\n3 4\n2 3\n1 1\n2 4\n1 4\n1 2\n2 2\n2 2\n1 1\n3 3\n1 2\n2 3\n2 3\n1 2\n1 4\n4 4\n2 2\n2 2\n4 4\n1 4\n1 1\n1 2\n4 4\n2 3\n2 4\n3 3\n1 4\n2 4\n2 3\n4 4\n4 4\n3 4\n2 2\n1 2\n1 1\n1 2\n3 3\n2 4\n1 3\n2 4\n1 1\n3 3\n3 4\n2 4\n1 4\n2 4\n1 2\n3 3\n1 4\n2 2\n2 4\n1 4\n1 4\n1 3\n3 4\n1 2\n2 3\n2 3\n3 4\n1 4\n4 4\n3 3\n2 4\n2 2\n1 2\n2 3\n1 2\n1 4\n1 3\n2 3\n4 4\n3 3\n1 2\n4 4\n2 4\n1 2\n2 4\n2 2\n3 4\n2 3\n2 3\n2 3",
"output": "4\n3\n1\n3\n2\n2\n1\n1\n3\n7\n1\n6\n7\n1\n3\n3\n2\n6\n2\n3\n1\n4\n7\n3\n1\n1\n1\n1\n3\n3\n3\n3\n7\n1\n1\n1\n1\n7\n1\n3\n1\n3\n4\n1\n7\n4\n3\n1\n1\n2\n1\n3\n1\n3\n1\n4\n6\n4\n1\n1\n2\n4\n7\n4\n3\n1\n7\n1\n4\n7\n7\n6\n2\n3\n3\n3\n2\n7\n1\n1\n4\n1\n3\n3\n3\n7\n6\n3\n1\n1\n3\n1\n4\n3\n4\n1\n2\n3\n3\n3"
}
] | 592 | 307,200 | 0 | 14,757 |
|
404 | Minesweeper 1D | [
"dp",
"implementation"
] | null | null | Game "Minesweeper 1D" is played on a line of squares, the line's height is 1 square, the line's width is *n* squares. Some of the squares contain bombs. If a square doesn't contain a bomb, then it contains a number from 0 to 2 — the total number of bombs in adjacent squares.
For example, the correct field to play looks like that: 001*2***101*. The cells that are marked with "*" contain bombs. Note that on the correct field the numbers represent the number of bombs in adjacent cells. For example, field 2* is not correct, because cell with value 2 must have two adjacent cells with bombs.
Valera wants to make a correct field to play "Minesweeper 1D". He has already painted a squared field with width of *n* cells, put several bombs on the field and wrote numbers into some cells. Now he wonders how many ways to fill the remaining cells with bombs and numbers are there if we should get a correct field in the end. | The first line contains sequence of characters without spaces *s*1*s*2... *s**n* (1<=≤<=*n*<=≤<=106), containing only characters "*", "?" and digits "0", "1" or "2". If character *s**i* equals "*", then the *i*-th cell of the field contains a bomb. If character *s**i* equals "?", then Valera hasn't yet decided what to put in the *i*-th cell. Character *s**i*, that is equal to a digit, represents the digit written in the *i*-th square. | Print a single integer — the number of ways Valera can fill the empty cells and get a correct field.
As the answer can be rather large, print it modulo 1000000007 (109<=+<=7). | [
"?01???\n",
"?\n",
"**12\n",
"1\n"
] | [
"4\n",
"2\n",
"0\n",
"0\n"
] | In the first test sample you can get the following correct fields: 001**1, 001***, 001*2*, 001*10. | [
{
"input": "?01???",
"output": "4"
},
{
"input": "?",
"output": "2"
},
{
"input": "**12",
"output": "0"
},
{
"input": "1",
"output": "0"
},
{
"input": "?01*??****",
"output": "4"
},
{
"input": "0",
"output": "1"
},
{
"input": "2",
"output": "0"
},
{
"input": "*",
"output": "1"
},
{
"input": "0*",
"output": "0"
},
{
"input": "0?",
"output": "1"
},
{
"input": "01",
"output": "0"
},
{
"input": "1*",
"output": "1"
},
{
"input": "1?",
"output": "1"
},
{
"input": "?1?",
"output": "2"
},
{
"input": "12",
"output": "0"
},
{
"input": "2*",
"output": "0"
},
{
"input": "2?",
"output": "0"
},
{
"input": "2??",
"output": "0"
},
{
"input": "?2?",
"output": "1"
},
{
"input": "?2*?2*??1*2**?2*1???*2???100?????*???*?*????0????2?*?*?1??1??*?01**2**1001??**??**??1*?*???00??**??*",
"output": "147483634"
},
{
"input": "00***???01",
"output": "0"
},
{
"input": "21?20*0000?2?22??0001*?1??12?20020200?**0*12?*221*0*1200*?0*11?022*110*2*2022120*2*2100*0?0*02?012?1",
"output": "0"
}
] | 46 | 0 | 0 | 14,762 |
|
750 | New Year and North Pole | [
"geometry",
"implementation"
] | null | null | In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40<=000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20<=000 kilometers.
Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of *n* parts. In the *i*-th part of his journey, Limak should move *t**i* kilometers in the direction represented by a string *dir**i* that is one of: "North", "South", "West", "East".
Limak isn’t sure whether the description is valid. You must help him to check the following conditions:
- If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. - If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. - The journey must end on the North Pole.
Check if the above conditions are satisfied and print "YES" or "NO" on a single line. | The first line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=50).
The *i*-th of next *n* lines contains an integer *t**i* and a string *dir**i* (1<=≤<=*t**i*<=≤<=106, ) — the length and the direction of the *i*-th part of the journey, according to the description Limak got. | Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. | [
"5\n7500 South\n10000 East\n3500 North\n4444 West\n4000 North\n",
"2\n15000 South\n4000 East\n",
"5\n20000 South\n1000 North\n1000000 West\n9000 North\n10000 North\n",
"3\n20000 South\n10 East\n20000 North\n",
"2\n1000 North\n1000 South\n",
"4\n50 South\n50 North\n15000 South\n15000 North\n"
] | [
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n"
] | Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. | [
{
"input": "5\n7500 South\n10000 East\n3500 North\n4444 West\n4000 North",
"output": "YES"
},
{
"input": "2\n15000 South\n4000 East",
"output": "NO"
},
{
"input": "5\n20000 South\n1000 North\n1000000 West\n9000 North\n10000 North",
"output": "YES"
},
{
"input": "3\n20000 South\n10 East\n20000 North",
"output": "NO"
},
{
"input": "2\n1000 North\n1000 South",
"output": "NO"
},
{
"input": "4\n50 South\n50 North\n15000 South\n15000 North",
"output": "YES"
},
{
"input": "1\n1 South",
"output": "NO"
},
{
"input": "1\n1 East",
"output": "NO"
},
{
"input": "2\n1000000 South\n1000000 North",
"output": "NO"
},
{
"input": "1\n149 South",
"output": "NO"
},
{
"input": "1\n16277 East",
"output": "NO"
},
{
"input": "1\n19701 South",
"output": "NO"
},
{
"input": "1\n3125 South",
"output": "NO"
},
{
"input": "1\n6549 South",
"output": "NO"
},
{
"input": "1\n2677 South",
"output": "NO"
},
{
"input": "1\n6101 South",
"output": "NO"
},
{
"input": "1\n9525 South",
"output": "NO"
},
{
"input": "1\n5653 South",
"output": "NO"
},
{
"input": "2\n15072 South\n15072 North",
"output": "YES"
},
{
"input": "2\n11200 South\n11200 North",
"output": "YES"
},
{
"input": "2\n14624 South\n14624 North",
"output": "YES"
},
{
"input": "2\n18048 South\n15452 West",
"output": "NO"
},
{
"input": "2\n1472 West\n4930 North",
"output": "NO"
},
{
"input": "2\n17600 South\n17600 North",
"output": "YES"
},
{
"input": "2\n8320 East\n16589 East",
"output": "NO"
},
{
"input": "2\n4448 South\n4448 North",
"output": "YES"
},
{
"input": "2\n576 South\n576 North",
"output": "YES"
},
{
"input": "3\n14186 South\n2291 West\n14186 North",
"output": "YES"
},
{
"input": "3\n10314 South\n15961 North\n5647 South",
"output": "NO"
},
{
"input": "3\n1035 East\n18143 South\n18143 North",
"output": "NO"
},
{
"input": "3\n17163 South\n7620 East\n17163 North",
"output": "YES"
},
{
"input": "3\n587 South\n17098 North\n16511 South",
"output": "NO"
},
{
"input": "3\n16715 North\n6576 West\n12132 South",
"output": "NO"
},
{
"input": "3\n7435 South\n245 North\n7190 North",
"output": "YES"
},
{
"input": "3\n3563 South\n2427 South\n5990 North",
"output": "YES"
},
{
"input": "3\n6987 South\n11904 East\n19951 East",
"output": "NO"
},
{
"input": "4\n13301 South\n5948 East\n9265 East\n6891 North",
"output": "NO"
},
{
"input": "4\n16725 South\n8129 South\n19530 West\n24854 North",
"output": "NO"
},
{
"input": "4\n149 South\n17607 West\n18306 South\n18455 North",
"output": "YES"
},
{
"input": "4\n16277 South\n19789 North\n4379 South\n867 North",
"output": "NO"
},
{
"input": "4\n19701 South\n13458 South\n3156 North\n30003 North",
"output": "NO"
},
{
"input": "4\n3125 South\n15640 East\n6125 East\n19535 South",
"output": "NO"
},
{
"input": "4\n6549 East\n5118 North\n12198 East\n5118 South",
"output": "NO"
},
{
"input": "4\n2677 East\n1891 West\n10974 West\n7511 North",
"output": "NO"
},
{
"input": "4\n6102 South\n8265 East\n13943 South\n20045 North",
"output": "NO"
},
{
"input": "5\n12416 South\n18116 North\n10553 West\n18435 West\n5700 South",
"output": "NO"
},
{
"input": "5\n15840 South\n7594 South\n13522 South\n2423 South\n3334 West",
"output": "NO"
},
{
"input": "5\n19264 East\n13968 East\n19595 North\n19115 North\n38710 South",
"output": "NO"
},
{
"input": "5\n15392 South\n3445 North\n18372 East\n10399 North\n4403 South",
"output": "NO"
},
{
"input": "5\n18816 South\n5627 West\n14045 East\n7091 East\n18816 North",
"output": "YES"
},
{
"input": "5\n2240 South\n15104 North\n118 West\n11079 East\n12864 South",
"output": "NO"
},
{
"input": "5\n5664 South\n1478 South\n18894 South\n2363 West\n26036 North",
"output": "NO"
},
{
"input": "5\n1792 South\n10956 East\n9159 South\n19055 West\n10951 North",
"output": "YES"
},
{
"input": "5\n12512 South\n13137 North\n7936 North\n7235 South\n1326 South",
"output": "NO"
},
{
"input": "6\n14635 North\n14477 South\n17250 North\n14170 East\n15166 South\n2242 South",
"output": "NO"
},
{
"input": "6\n10763 North\n3954 West\n7515 North\n18158 West\n6644 South\n11634 South",
"output": "NO"
},
{
"input": "6\n14187 South\n13432 North\n6292 East\n14850 West\n10827 South\n9639 East",
"output": "NO"
},
{
"input": "6\n10315 South\n15614 South\n5069 West\n6134 South\n7713 North\n24350 North",
"output": "NO"
},
{
"input": "6\n1035 South\n9283 East\n15333 South\n2826 South\n19191 North\n3 North",
"output": "YES"
},
{
"input": "6\n17163 West\n11465 North\n14110 South\n6814 North\n3373 East\n4169 South",
"output": "NO"
},
{
"input": "6\n587 South\n942 West\n183 North\n18098 North\n260 East\n17694 South",
"output": "NO"
},
{
"input": "6\n16715 West\n3124 East\n3152 East\n14790 East\n11738 West\n11461 East",
"output": "NO"
},
{
"input": "6\n7435 South\n12602 South\n1929 East\n6074 East\n15920 West\n20037 North",
"output": "NO"
},
{
"input": "7\n13750 South\n6645 South\n18539 East\n5713 North\n1580 North\n10012 West\n13102 North",
"output": "NO"
},
{
"input": "7\n9878 West\n8827 East\n1508 West\n9702 North\n5763 North\n9755 North\n10034 South",
"output": "NO"
},
{
"input": "7\n13302 West\n2496 North\n284 West\n6394 East\n9945 North\n12603 West\n12275 North",
"output": "NO"
},
{
"input": "7\n16726 East\n19270 West\n6357 South\n17678 East\n14127 East\n12347 South\n6005 East",
"output": "NO"
},
{
"input": "7\n150 South\n1452 North\n9326 North\n1666 West\n18309 East\n19386 East\n8246 West",
"output": "NO"
},
{
"input": "7\n16278 South\n10929 South\n8103 East\n18358 West\n2492 West\n11834 South\n39041 North",
"output": "NO"
},
{
"input": "7\n19702 South\n13111 East\n6880 East\n9642 South\n6674 West\n18874 East\n1112 North",
"output": "NO"
},
{
"input": "7\n3126 South\n6780 North\n9848 West\n6334 North\n10856 West\n14425 West\n10649 East",
"output": "NO"
},
{
"input": "7\n6550 South\n8962 West\n15921 South\n17618 North\n15038 South\n1465 North\n18426 North",
"output": "NO"
},
{
"input": "8\n12864 South\n3005 West\n16723 West\n17257 West\n12187 East\n12976 South\n1598 North\n24242 North",
"output": "NO"
},
{
"input": "8\n8992 South\n12483 North\n15500 South\n1245 South\n9073 East\n12719 East\n3839 East\n7130 South",
"output": "NO"
},
{
"input": "8\n12416 North\n14665 South\n14277 North\n2129 South\n13255 East\n19759 South\n10272 West\n9860 North",
"output": "NO"
},
{
"input": "8\n15840 South\n4142 East\n17246 North\n13413 North\n4733 West\n15311 North\n12514 South\n17616 South",
"output": "NO"
},
{
"input": "8\n19264 South\n10516 North\n3319 East\n17401 East\n1620 West\n2350 West\n6243 North\n2505 North",
"output": "YES"
},
{
"input": "8\n15392 South\n7290 West\n2096 West\n14093 East\n5802 South\n2094 North\n8484 East\n19100 North",
"output": "NO"
},
{
"input": "8\n6113 South\n16767 East\n5064 South\n5377 West\n17280 South\n1838 West\n2213 West\n28457 North",
"output": "NO"
},
{
"input": "8\n2241 West\n18949 South\n11137 South\n2069 West\n14166 South\n1581 South\n4455 South\n50288 North",
"output": "NO"
},
{
"input": "8\n5665 South\n8426 East\n9914 North\n13353 South\n18349 North\n4429 East\n18184 North\n27429 South",
"output": "NO"
},
{
"input": "9\n11979 South\n2470 East\n10716 North\n12992 East\n15497 West\n15940 North\n8107 West\n18934 East\n6993 South",
"output": "NO"
},
{
"input": "9\n8107 South\n4652 North\n9493 North\n16980 West\n12383 West\n2980 West\n17644 South\n11043 West\n11447 North",
"output": "NO"
},
{
"input": "9\n18827 South\n18321 West\n8270 East\n968 West\n16565 West\n15427 North\n4077 North\n18960 North\n19006 West",
"output": "NO"
},
{
"input": "9\n14955 West\n503 North\n18535 West\n4956 South\n8044 South\n2467 East\n13615 East\n6877 East\n3460 North",
"output": "NO"
},
{
"input": "9\n18379 South\n9980 South\n17311 West\n8944 South\n4930 South\n18019 South\n48 West\n14794 South\n75046 North",
"output": "NO"
},
{
"input": "9\n14507 East\n12162 East\n16088 South\n5636 North\n9112 North\n5058 East\n9585 South\n2712 East\n10925 North",
"output": "NO"
},
{
"input": "9\n5227 East\n8936 North\n6353 North\n16920 North\n591 North\n4802 South\n8722 North\n3333 West\n36720 South",
"output": "NO"
},
{
"input": "9\n1355 North\n15309 West\n17834 North\n13612 East\n17477 North\n4546 North\n18260 East\n15442 North\n56654 South",
"output": "NO"
},
{
"input": "9\n4779 South\n4787 East\n3907 East\n4896 East\n1659 East\n4289 West\n4693 West\n3359 East\n4779 North",
"output": "YES"
},
{
"input": "1\n80000 South",
"output": "NO"
},
{
"input": "2\n40000 South\n20000 North",
"output": "NO"
},
{
"input": "1\n40000 South",
"output": "NO"
},
{
"input": "2\n20001 South\n20001 North",
"output": "NO"
},
{
"input": "4\n10000 South\n20000 South\n10000 North\n20000 North",
"output": "NO"
},
{
"input": "3\n10 South\n20 North\n10 North",
"output": "NO"
},
{
"input": "3\n1000 South\n1001 North\n1 North",
"output": "NO"
},
{
"input": "2\n20000 South\n20000 West",
"output": "NO"
},
{
"input": "3\n10000 South\n20000 South\n10000 North",
"output": "NO"
},
{
"input": "2\n1 East\n1 North",
"output": "NO"
},
{
"input": "2\n20000 West\n20000 West",
"output": "NO"
},
{
"input": "2\n80000 South\n20000 North",
"output": "NO"
},
{
"input": "2\n19999 South\n20001 South",
"output": "NO"
},
{
"input": "3\n500 South\n1000 North\n500 North",
"output": "NO"
},
{
"input": "1\n400000 South",
"output": "NO"
},
{
"input": "2\n40000 South\n80000 North",
"output": "NO"
},
{
"input": "2\n100 West\n100 North",
"output": "NO"
},
{
"input": "2\n40000 South\n40000 North",
"output": "NO"
},
{
"input": "2\n30000 South\n10000 North",
"output": "NO"
},
{
"input": "2\n20000 South\n40000 North",
"output": "NO"
},
{
"input": "10\n20000 South\n20000 North\n20000 South\n20000 North\n20000 South\n20000 North\n20000 South\n20000 North\n20000 South\n20000 North",
"output": "YES"
},
{
"input": "2\n40001 South\n40001 North",
"output": "NO"
},
{
"input": "2\n40001 South\n1 North",
"output": "NO"
},
{
"input": "2\n50000 South\n50000 North",
"output": "NO"
},
{
"input": "2\n30000 South\n30000 South",
"output": "NO"
},
{
"input": "2\n10000 South\n50000 North",
"output": "NO"
},
{
"input": "4\n15000 South\n15000 South\n15000 North\n15000 North",
"output": "NO"
},
{
"input": "3\n50 South\n100 North\n50 North",
"output": "NO"
},
{
"input": "2\n20001 South\n1 North",
"output": "NO"
},
{
"input": "3\n5 South\n6 North\n1 South",
"output": "NO"
},
{
"input": "1\n20000 South",
"output": "NO"
},
{
"input": "4\n1 South\n20000 South\n1 North\n20000 North",
"output": "NO"
},
{
"input": "2\n30000 South\n30000 North",
"output": "NO"
},
{
"input": "3\n1 South\n2 North\n1 South",
"output": "NO"
},
{
"input": "2\n60000 South\n60000 North",
"output": "NO"
},
{
"input": "2\n50000 South\n10000 North",
"output": "NO"
},
{
"input": "1\n5 North",
"output": "NO"
},
{
"input": "2\n20010 South\n19990 North",
"output": "NO"
},
{
"input": "3\n20000 South\n1 South\n20000 North",
"output": "NO"
},
{
"input": "3\n1 South\n2 North\n39999 North",
"output": "NO"
},
{
"input": "3\n10 South\n20 North\n10 South",
"output": "NO"
},
{
"input": "3\n1 South\n2 North\n1 North",
"output": "NO"
},
{
"input": "3\n2000 South\n19000 South\n19000 South",
"output": "NO"
},
{
"input": "6\n15000 South\n15000 South\n15000 South\n15000 North\n15000 North\n15000 North",
"output": "NO"
},
{
"input": "3\n1 South\n1 North\n1 East",
"output": "NO"
},
{
"input": "2\n1 West\n1 North",
"output": "NO"
},
{
"input": "3\n1 South\n123456 West\n1 North",
"output": "YES"
}
] | 30 | 0 | 0 | 14,820 |
|
379 | New Year Ratings Change | [
"greedy",
"sortings"
] | null | null | One very well-known internet resource site (let's call it X) has come up with a New Year adventure. Specifically, they decided to give ratings to all visitors.
There are *n* users on the site, for each user we know the rating value he wants to get as a New Year Present. We know that user *i* wants to get at least *a**i* rating units as a present.
The X site is administered by very creative and thrifty people. On the one hand, they want to give distinct ratings and on the other hand, the total sum of the ratings in the present must be as small as possible.
Help site X cope with the challenging task of rating distribution. Find the optimal distribution. | The first line contains integer *n* (1<=≤<=*n*<=≤<=3·105) — the number of users on the site. The next line contains integer sequence *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109). | Print a sequence of integers *b*1,<=*b*2,<=...,<=*b**n*. Number *b**i* means that user *i* gets *b**i* of rating as a present. The printed sequence must meet the problem conditions.
If there are multiple optimal solutions, print any of them. | [
"3\n5 1 1\n",
"1\n1000000000\n"
] | [
"5 1 2\n",
"1000000000\n"
] | none | [
{
"input": "3\n5 1 1",
"output": "5 1 2"
},
{
"input": "1\n1000000000",
"output": "1000000000"
},
{
"input": "10\n1 1 1 1 1 1 1 1 1 1",
"output": "1 2 3 4 5 6 7 8 9 10"
},
{
"input": "10\n1 10 1 10 1 1 7 8 6 7",
"output": "1 10 2 11 3 4 7 9 6 8"
},
{
"input": "10\n20 19 12 1 12 15 2 12 6 10",
"output": "20 19 12 1 13 15 2 14 6 10"
},
{
"input": "10\n4 5 10 5 2 14 15 6 10 6",
"output": "4 5 10 6 2 14 15 7 11 8"
}
] | 1,000 | 29,593,600 | 0 | 14,863 |
|
409 | 000001 | [
"*special"
] | null | null | The input contains a single integer *a* (1<=≤<=*a*<=≤<=64).
Output a single integer. | The input contains a single integer *a* (1<=≤<=*a*<=≤<=64). | Output a single integer. | [
"2\n",
"4\n",
"27\n",
"42\n"
] | [
"1\n",
"2\n",
"5\n",
"6\n"
] | none | [
{
"input": "2",
"output": "1"
},
{
"input": "4",
"output": "2"
},
{
"input": "27",
"output": "5"
},
{
"input": "42",
"output": "6"
},
{
"input": "1",
"output": "1"
},
{
"input": "3",
"output": "1"
},
{
"input": "64",
"output": "267"
},
{
"input": "5",
"output": "1"
},
{
"input": "6",
"output": "2"
},
{
"input": "7",
"output": "1"
},
{
"input": "8",
"output": "5"
},
{
"input": "9",
"output": "2"
},
{
"input": "10",
"output": "2"
},
{
"input": "11",
"output": "1"
},
{
"input": "12",
"output": "5"
},
{
"input": "13",
"output": "1"
},
{
"input": "14",
"output": "2"
},
{
"input": "15",
"output": "1"
},
{
"input": "16",
"output": "14"
},
{
"input": "17",
"output": "1"
},
{
"input": "18",
"output": "5"
},
{
"input": "19",
"output": "1"
},
{
"input": "20",
"output": "5"
},
{
"input": "21",
"output": "2"
},
{
"input": "22",
"output": "2"
},
{
"input": "23",
"output": "1"
},
{
"input": "24",
"output": "15"
},
{
"input": "25",
"output": "2"
},
{
"input": "26",
"output": "2"
},
{
"input": "28",
"output": "4"
},
{
"input": "29",
"output": "1"
},
{
"input": "30",
"output": "4"
},
{
"input": "31",
"output": "1"
},
{
"input": "32",
"output": "51"
},
{
"input": "33",
"output": "1"
},
{
"input": "34",
"output": "2"
},
{
"input": "35",
"output": "1"
},
{
"input": "36",
"output": "14"
},
{
"input": "37",
"output": "1"
},
{
"input": "38",
"output": "2"
},
{
"input": "39",
"output": "2"
},
{
"input": "40",
"output": "14"
},
{
"input": "41",
"output": "1"
},
{
"input": "43",
"output": "1"
},
{
"input": "44",
"output": "4"
},
{
"input": "45",
"output": "2"
},
{
"input": "46",
"output": "2"
},
{
"input": "47",
"output": "1"
},
{
"input": "48",
"output": "52"
},
{
"input": "49",
"output": "2"
},
{
"input": "50",
"output": "5"
},
{
"input": "51",
"output": "1"
},
{
"input": "52",
"output": "5"
},
{
"input": "53",
"output": "1"
},
{
"input": "54",
"output": "15"
},
{
"input": "55",
"output": "2"
},
{
"input": "56",
"output": "13"
},
{
"input": "57",
"output": "2"
},
{
"input": "58",
"output": "2"
},
{
"input": "59",
"output": "1"
},
{
"input": "60",
"output": "13"
},
{
"input": "61",
"output": "1"
},
{
"input": "62",
"output": "2"
},
{
"input": "63",
"output": "4"
}
] | 46 | 0 | 3 | 14,879 |
|
453 | Little Pony and Lord Tirek | [
"data structures"
] | null | null | Lord Tirek is a centaur and the main antagonist in the season four finale episodes in the series "My Little Pony: Friendship Is Magic". In "Twilight's Kingdom" (Part 1), Tirek escapes from Tartarus and drains magic from ponies to grow stronger.
The core skill of Tirek is called Absorb Mana. It takes all mana from a magic creature and gives them to the caster.
Now to simplify the problem, assume you have *n* ponies (numbered from 1 to *n*). Each pony has three attributes:
- *s**i* : amount of mana that the pony has at time 0; - *m**i* : maximum mana that the pony can have; - *r**i* : mana regeneration per unit time.
Lord Tirek will do *m* instructions, each of them can be described with three integers: *t**i*,<=*l**i*,<=*r**i*. The instruction means that at time *t**i*, Tirek will use Absorb Mana on ponies with numbers from *l**i* to *r**i* (both borders inclusive). We'll give you all the *m* instructions in order, count how much mana Tirek absorbs for each instruction. | The first line contains an integer *n* (1<=≤<=*n*<=≤<=105) — the number of ponies. Each of the next *n* lines contains three integers *s**i*,<=*m**i*,<=*r**i* (0<=≤<=*s**i*<=≤<=*m**i*<=≤<=105; 0<=≤<=*r**i*<=≤<=105), describing a pony.
The next line contains an integer *m* (1<=≤<=*m*<=≤<=105) — the number of instructions. Each of the next *m* lines contains three integers *t**i*,<=*l**i*,<=*r**i* (0<=≤<=*t**i*<=≤<=109; 1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*), describing an instruction of Lord Tirek. The instructions are given in strictly increasing order of *t**i* (all *t**i* are distinct). | For each instruction, output a single line which contains a single integer, the total mana absorbed in this instruction. | [
"5\n0 10 1\n0 12 1\n0 20 1\n0 12 1\n0 10 1\n2\n5 1 5\n19 1 5\n"
] | [
"25\n58\n"
] | Every pony starts with zero mana. For the first instruction, each pony has 5 mana, so you get 25 mana in total and each pony has 0 mana after the first instruction.
For the second instruction, pony 3 has 14 mana and other ponies have mana equal to their *m*<sub class="lower-index">*i*</sub>. | [] | 46 | 0 | 0 | 14,883 |
|
48 | The Race | [
"math"
] | C. The Race | 2 | 256 | Every year a race takes place on the motorway between cities A and B. This year Vanya decided to take part in the race and drive his own car that has been around and bears its own noble name — The Huff-puffer.
So, Vasya leaves city A on the Huff-puffer, besides, at the very beginning he fills the petrol tank with α liters of petrol (α<=≥<=10 is Vanya's favorite number, it is not necessarily integer). Petrol stations are located on the motorway at an interval of 100 kilometers, i.e. the first station is located 100 kilometers away from the city A, the second one is 200 kilometers away from the city A, the third one is 300 kilometers away from the city A and so on. The Huff-puffer spends 10 liters of petrol every 100 kilometers.
Vanya checks the petrol tank every time he passes by a petrol station. If the petrol left in the tank is not enough to get to the next station, Vanya fills the tank with α liters of petrol. Otherwise, he doesn't stop at the station and drives on.
For example, if α<==<=43.21, then the car will be fuelled up for the first time at the station number 4, when there'll be 3.21 petrol liters left. After the fuelling up the car will have 46.42 liters. Then Vanya stops at the station number 8 and ends up with 6.42<=+<=43.21<==<=49.63 liters. The next stop is at the station number 12, 9.63<=+<=43.21<==<=52.84. The next stop is at the station number 17 and so on.
You won't believe this but the Huff-puffer has been leading in the race! Perhaps it is due to unexpected snow. Perhaps it is due to video cameras that have been installed along the motorway which register speed limit breaking. Perhaps it is due to the fact that Vanya threatened to junk the Huff-puffer unless the car wins. Whatever the reason is, the Huff-puffer is leading, and jealous people together with other contestants wrack their brains trying to think of a way to stop that outrage.
One way to do this is to mine the next petrol station where Vanya will stop. Your task is to calculate at which station this will happen and warn Vanya. You don't know the α number, however, you are given the succession of the numbers of the stations where Vanya has stopped. Find the number of the station where the next stop will be. | The first line contains an integer *n* (1<=≤<=*n*<=≤<=1000) which represents the number of petrol stations where Vanya has stopped. The next line has *n* space-separated integers which represent the numbers of the stations. The numbers are positive and do not exceed 106, they are given in the increasing order. No two numbers in the succession match. It is guaranteed that there exists at least one number α<=≥<=10, to which such a succession of stops corresponds. | Print in the first line "unique" (without quotes) if the answer can be determined uniquely. In the second line print the number of the station where the next stop will take place. If the answer is not unique, print in the first line "not unique". | [
"3\n1 2 4\n",
"2\n1 2\n"
] | [
"unique\n5\n",
"not unique\n"
] | In the second example the answer is not unique. For example, if α = 10, we'll have such a sequence as 1, 2, 3, and if α = 14, the sequence will be 1, 2, 4. | [
{
"input": "3\n1 2 4",
"output": "unique\n5"
},
{
"input": "2\n1 2",
"output": "not unique"
},
{
"input": "1\n5",
"output": "not unique"
},
{
"input": "3\n1 3 4",
"output": "unique\n6"
},
{
"input": "5\n1 2 3 5 6",
"output": "unique\n7"
},
{
"input": "6\n1 2 3 5 6 7",
"output": "not unique"
},
{
"input": "10\n1 2 4 5 7 8 9 11 12 14",
"output": "unique\n15"
},
{
"input": "10\n1 3 5 6 8 10 12 13 15 17",
"output": "not unique"
},
{
"input": "9\n2 5 7 10 12 15 17 20 22",
"output": "unique\n25"
},
{
"input": "10\n7 14 21 28 35 42 49 56 63 70",
"output": "not unique"
},
{
"input": "15\n5 11 16 22 28 33 39 45 50 56 62 67 73 79 84",
"output": "unique\n90"
},
{
"input": "17\n5 11 16 22 28 33 39 45 50 56 62 67 73 79 84 90 96",
"output": "unique\n101"
},
{
"input": "15\n1 3 4 6 8 9 11 12 14 16 17 19 21 22 24",
"output": "unique\n25"
},
{
"input": "16\n1 3 4 6 8 9 11 12 14 16 17 19 21 22 24 25",
"output": "unique\n27"
},
{
"input": "17\n1 3 4 6 8 9 11 12 14 16 17 19 21 22 24 25 27",
"output": "unique\n29"
},
{
"input": "18\n1 3 4 6 8 9 11 12 14 16 17 19 21 22 24 25 27 29",
"output": "unique\n30"
},
{
"input": "19\n1 3 4 6 8 9 11 12 14 16 17 19 21 22 24 25 27 29 30",
"output": "unique\n32"
},
{
"input": "20\n1 3 4 6 8 9 11 12 14 16 17 19 21 22 24 25 27 29 30 32",
"output": "not unique"
},
{
"input": "18\n49999 99998 149998 199997 249996 299996 349995 399994 449994 499993 549992 599992 649991 699990 749990 799989 849988 899988",
"output": "unique\n949987"
},
{
"input": "20\n49999 99998 149998 199997 249996 299996 349995 399994 449994 499993 549992 599992 649991 699990 749990 799989 849988 899988 949987 999986",
"output": "unique\n1049986"
},
{
"input": "33\n9 19 29 39 49 59 69 79 89 99 109 119 129 139 149 159 168 178 188 198 208 218 228 238 248 258 268 278 288 298 308 318 327",
"output": "unique\n337"
},
{
"input": "46\n40 81 122 162 203 244 284 325 366 406 447 488 528 569 610 650 691 732 772 813 854 894 935 976 1016 1057 1098 1138 1179 1220 1260 1301 1342 1382 1423 1464 1504 1545 1586 1626 1667 1708 1748 1789 1830 1870",
"output": "unique\n1911"
},
{
"input": "50\n19876 39753 59629 79506 99382 119259 139135 159012 178889 198765 218642 238518 258395 278271 298148 318025 337901 357778 377654 397531 417407 437284 457160 477037 496914 516790 536667 556543 576420 596296 616173 636050 655926 675803 695679 715556 735432 755309 775186 795062 814939 834815 854692 874568 894445 914321 934198 954075 973951 993828",
"output": "unique\n1013704"
},
{
"input": "50\n564 1129 1693 2258 2822 3387 3951 4516 5080 5645 6210 6774 7339 7903 8468 9032 9597 10161 10726 11290 11855 12420 12984 13549 14113 14678 15242 15807 16371 16936 17500 18065 18630 19194 19759 20323 20888 21452 22017 22581 23146 23710 24275 24840 25404 25969 26533 27098 27662 28227",
"output": "unique\n28791"
},
{
"input": "76\n342 684 1027 1369 1711 2054 2396 2738 3081 3423 3765 4108 4450 4792 5135 5477 5819 6162 6504 6846 7189 7531 7873 8216 8558 8900 9243 9585 9927 10270 10612 10954 11297 11639 11981 12324 12666 13009 13351 13693 14036 14378 14720 15063 15405 15747 16090 16432 16774 17117 17459 17801 18144 18486 18828 19171 19513 19855 20198 20540 20882 21225 21567 21909 22252 22594 22936 23279 23621 23963 24306 24648 24991 25333 25675 26018",
"output": "unique\n26360"
},
{
"input": "100\n1 3 4 6 8 9 11 12 14 16 17 19 21 22 24 25 27 29 30 32 33 35 37 38 40 42 43 45 46 48 50 51 53 55 56 58 59 61 63 64 66 67 69 71 72 74 76 77 79 80 82 84 85 87 88 90 92 93 95 97 98 100 101 103 105 106 108 110 111 113 114 116 118 119 121 122 124 126 127 129 131 132 134 135 137 139 140 142 144 145 147 148 150 152 153 155 156 158 160 161",
"output": "unique\n163"
},
{
"input": "101\n3 7 10 14 18 21 25 28 32 36 39 43 46 50 54 57 61 64 68 72 75 79 82 86 90 93 97 100 104 108 111 115 118 122 126 129 133 137 140 144 147 151 155 158 162 165 169 173 176 180 183 187 191 194 198 201 205 209 212 216 219 223 227 230 234 237 241 245 248 252 255 259 263 266 270 274 277 281 284 288 292 295 299 302 306 310 313 317 320 324 328 331 335 338 342 346 349 353 356 360 364",
"output": "unique\n367"
}
] | 1,340 | 307,200 | 3.664428 | 14,884 |
963 | Cutting Rectangle | [
"brute force",
"math",
"number theory"
] | null | null | A rectangle with sides $A$ and $B$ is cut into rectangles with cuts parallel to its sides. For example, if $p$ horizontal and $q$ vertical cuts were made, $(p + 1) \cdot (q + 1)$ rectangles were left after the cutting. After the cutting, rectangles were of $n$ different types. Two rectangles are different if at least one side of one rectangle isn't equal to the corresponding side of the other. Note that the rectangle can't be rotated, this means that rectangles $a \times b$ and $b \times a$ are considered different if $a \neq b$.
For each type of rectangles, lengths of the sides of rectangles are given along with the amount of the rectangles of this type that were left after cutting the initial rectangle.
Calculate the amount of pairs $(A; B)$ such as the given rectangles could be created by cutting the rectangle with sides of lengths $A$ and $B$. Note that pairs $(A; B)$ and $(B; A)$ are considered different when $A \neq B$. | The first line consists of a single integer $n$ ($1 \leq n \leq 2 \cdot 10^{5}$) — amount of different types of rectangles left after cutting the initial rectangle.
The next $n$ lines each consist of three integers $w_{i}, h_{i}, c_{i}$ $(1 \leq w_{i}, h_{i}, c_{i} \leq 10^{12})$ — the lengths of the sides of the rectangles of this type and the amount of the rectangles of this type.
It is guaranteed that the rectangles of the different types are different. | Output one integer — the answer to the problem. | [
"1\n1 1 9\n",
"2\n2 3 20\n2 4 40\n",
"2\n1 2 5\n2 3 5\n"
] | [
"3\n",
"6\n",
"0\n"
] | In the first sample there are three suitable pairs: $(1; 9)$, $(3; 3)$ and $(9; 1)$.
In the second sample case there are 6 suitable pairs: $(2; 220)$, $(4; 110)$, $(8; 55)$, $(10; 44)$, $(20; 22)$ and $(40; 11)$.
Here the sample of cut for $(20; 22)$.
The third sample has no suitable pairs. | [
{
"input": "1\n1 1 9",
"output": "3"
},
{
"input": "2\n2 3 20\n2 4 40",
"output": "6"
},
{
"input": "2\n1 2 5\n2 3 5",
"output": "0"
}
] | 0 | 0 | -1 | 14,885 |
|
23 | Oranges and Apples | [
"constructive algorithms",
"sortings"
] | C. Oranges and Apples | 1 | 256 | In 2*N*<=-<=1 boxes there are apples and oranges. Your task is to choose *N* boxes so, that they will contain not less than half of all the apples and not less than half of all the oranges. | The first input line contains one number *T* — amount of tests. The description of each test starts with a natural number *N* — amount of boxes. Each of the following 2*N*<=-<=1 lines contains numbers *a**i* and *o**i* — amount of apples and oranges in the *i*-th box (0<=≤<=*a**i*,<=*o**i*<=≤<=109). The sum of *N* in all the tests in the input doesn't exceed 105. All the input numbers are integer. | For each test output two lines. In the first line output YES, if it's possible to choose *N* boxes, or NO otherwise. If the answer is positive output in the second line *N* numbers — indexes of the chosen boxes. Boxes are numbered from 1 in the input order. Otherwise leave the second line empty. Separate the numbers with one space. | [
"2\n2\n10 15\n5 7\n20 18\n1\n0 0\n"
] | [
"YES\n1 3\nYES\n1\n"
] | none | [
{
"input": "2\n2\n10 15\n5 7\n20 18\n1\n0 0",
"output": "YES\n3 1\nYES\n1"
}
] | 2,000 | 24,064,000 | 0 | 14,907 |
187 | Permutations | [
"greedy"
] | null | null | Happy PMP is freshman and he is learning about algorithmic problems. He enjoys playing algorithmic games a lot.
One of the seniors gave Happy PMP a nice game. He is given two permutations of numbers 1 through *n* and is asked to convert the first one to the second. In one move he can remove the last number from the permutation of numbers and inserts it back in an arbitrary position. He can either insert last number between any two consecutive numbers, or he can place it at the beginning of the permutation.
Happy PMP has an algorithm that solves the problem. But it is not fast enough. He wants to know the minimum number of moves to convert the first permutation to the second. | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=2·105) — the quantity of the numbers in the both given permutations.
Next line contains *n* space-separated integers — the first permutation. Each number between 1 to *n* will appear in the permutation exactly once.
Next line describe the second permutation in the same format. | Print a single integer denoting the minimum number of moves required to convert the first permutation to the second. | [
"3\n3 2 1\n1 2 3\n",
"5\n1 2 3 4 5\n1 5 2 3 4\n",
"5\n1 5 2 3 4\n1 2 3 4 5\n"
] | [
"2\n",
"1\n",
"3\n"
] | In the first sample, he removes number 1 from end of the list and places it at the beginning. After that he takes number 2 and places it between 1 and 3.
In the second sample, he removes number 5 and inserts it after 1.
In the third sample, the sequence of changes are like this:
- 1 5 2 3 4 - 1 4 5 2 3 - 1 3 4 5 2 - 1 2 3 4 5 | [
{
"input": "3\n3 2 1\n1 2 3",
"output": "2"
},
{
"input": "5\n1 2 3 4 5\n1 5 2 3 4",
"output": "1"
},
{
"input": "5\n1 5 2 3 4\n1 2 3 4 5",
"output": "3"
},
{
"input": "1\n1\n1",
"output": "0"
},
{
"input": "7\n6 1 7 3 4 5 2\n6 1 7 3 4 5 2",
"output": "0"
},
{
"input": "10\n5 8 1 10 3 6 2 9 7 4\n4 2 6 3 1 9 10 5 8 7",
"output": "8"
},
{
"input": "10\n1 6 10 3 4 9 2 5 8 7\n7 5 1 6 10 3 4 8 9 2",
"output": "3"
},
{
"input": "10\n2 1 10 3 7 8 5 6 9 4\n6 9 2 4 1 10 3 7 8 5",
"output": "3"
},
{
"input": "10\n8 2 10 3 4 6 1 7 9 5\n8 2 10 3 4 6 1 7 9 5",
"output": "0"
},
{
"input": "20\n1 12 9 6 11 13 2 8 20 7 16 19 4 18 3 15 10 17 14 5\n5 14 17 10 15 3 18 4 19 16 7 20 8 2 13 11 6 9 12 1",
"output": "19"
}
] | 186 | 23,142,400 | 0 | 14,908 |
|
366 | Dima and Magic Guitar | [
"brute force",
"implementation",
"math"
] | null | null | Dima loves Inna very much. He decided to write a song for her. Dima has a magic guitar with *n* strings and *m* frets. Dima makes the guitar produce sounds like that: to play a note, he needs to hold one of the strings on one of the frets and then pull the string. When Dima pulls the *i*-th string holding it on the *j*-th fret the guitar produces a note, let's denote it as *a**ij*. We know that Dima's guitar can produce *k* distinct notes. It is possible that some notes can be produced in multiple ways. In other words, it is possible that *a**ij*<==<=*a**pq* at (*i*,<=*j*)<=≠<=(*p*,<=*q*).
Dima has already written a song — a sequence of *s* notes. In order to play the song, you need to consecutively produce the notes from the song on the guitar. You can produce each note in any available way. Dima understood that there are many ways to play a song and he wants to play it so as to make the song look as complicated as possible (try to act like Cobein).
We'll represent a way to play a song as a sequence of pairs (*x**i*,<=*y**i*) (1<=≤<=*i*<=≤<=*s*), such that the *x**i*-th string on the *y**i*-th fret produces the *i*-th note from the song. The complexity of moving between pairs (*x*1,<=*y*1) and (*x*2,<=*y*2) equals + . The complexity of a way to play a song is the maximum of complexities of moving between adjacent pairs.
Help Dima determine the maximum complexity of the way to play his song! The guy's gotta look cool! | The first line of the input contains four integers *n*, *m*, *k* and *s* (1<=≤<=*n*,<=*m*<=≤<=2000,<=1<=≤<=*k*<=≤<=9,<=2<=≤<=*s*<=≤<=105).
Then follow *n* lines, each containing *m* integers *a**ij* (1<=≤<=*a**ij*<=≤<=*k*). The number in the *i*-th row and the *j*-th column (*a**ij*) means a note that the guitar produces on the *i*-th string and the *j*-th fret.
The last line of the input contains *s* integers *q**i* (1<=≤<=*q**i*<=≤<=*k*) — the sequence of notes of the song. | In a single line print a single number — the maximum possible complexity of the song. | [
"4 6 5 7\n3 1 2 2 3 1\n3 2 2 2 5 5\n4 2 2 2 5 3\n3 2 2 1 4 3\n2 3 1 4 1 5 1\n",
"4 4 9 5\n4 7 9 5\n1 2 1 7\n8 3 4 9\n5 7 7 2\n7 1 9 2 5\n"
] | [
"8\n",
"4\n"
] | none | [
{
"input": "4 6 5 7\n3 1 2 2 3 1\n3 2 2 2 5 5\n4 2 2 2 5 3\n3 2 2 1 4 3\n2 3 1 4 1 5 1",
"output": "8"
},
{
"input": "4 4 9 5\n4 7 9 5\n1 2 1 7\n8 3 4 9\n5 7 7 2\n7 1 9 2 5",
"output": "4"
},
{
"input": "5 5 2 2\n2 2 2 1 2\n2 1 2 2 2\n2 2 2 2 2\n1 2 2 2 2\n2 2 2 2 1\n1 1",
"output": "6"
},
{
"input": "5 5 2 2\n2 1 2 2 2\n2 2 2 2 2\n2 2 2 2 1\n2 2 2 2 2\n1 2 2 2 2\n1 1",
"output": "6"
},
{
"input": "11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2",
"output": "14"
},
{
"input": "1 10 9 5\n1 2 3 4 5 6 7 8 9 1\n1 1 9 2 3",
"output": "9"
},
{
"input": "10 1 9 5\n1\n2\n3\n4\n5\n6\n7\n8\n9\n1\n1 1 9 2 3",
"output": "9"
}
] | 61 | 0 | 0 | 14,917 |
|
175 | Geometry Horse | [
"greedy",
"implementation",
"sortings",
"two pointers"
] | null | null | Vasya plays the Geometry Horse.
The game goal is to destroy geometric figures of the game world. A certain number of points is given for destroying each figure depending on the figure type and the current factor value.
There are *n* types of geometric figures. The number of figures of type *k**i* and figure cost *c**i* is known for each figure type. A player gets *c**i*·*f* points for destroying one figure of type *i*, where *f* is the current factor. The factor value can be an integer number from 1 to *t*<=+<=1, inclusive. At the beginning of the game the factor value is equal to 1. The factor is set to *i*<=+<=1 after destruction of *p**i* (1<=≤<=*i*<=≤<=*t*) figures, so the (*p**i*<=+<=1)-th figure to be destroyed is considered with factor equal to *i*<=+<=1.
Your task is to determine the maximum number of points Vasya can get after he destroys all figures. Take into account that Vasya is so tough that he can destroy figures in any order chosen by him. | The first line contains the only integer number *n* (1<=≤<=*n*<=≤<=100) — the number of figure types.
Each of the following *n* lines contains two integer numbers *k**i* and *c**i* (1<=≤<=*k**i*<=≤<=109,<=0<=≤<=*c**i*<=≤<=1000), separated with space — the number of figures of the *i*-th type and the cost of one *i*-type figure, correspondingly.
The next line contains the only integer number *t* (1<=≤<=*t*<=≤<=100) — the number that describe the factor's changes.
The next line contains *t* integer numbers *p**i* (1<=≤<=*p*1<=<<=*p*2<=<<=...<=<<=*p**t*<=≤<=1012), separated with spaces.
Please, do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator. | Print the only number — the maximum number of points Vasya can get. | [
"1\n5 10\n2\n3 6\n",
"2\n3 8\n5 10\n1\n20\n"
] | [
"70",
"74"
] | In the first example Vasya destroys three figures first and gets 3·1·10 = 30 points. Then the factor will become equal to 2 and after destroying the last two figures Vasya will get 2·2·10 = 40 points. As a result Vasya will get 70 points.
In the second example all 8 figures will be destroyed with factor 1, so Vasya will get (3·8 + 5·10)·1 = 74 points. | [
{
"input": "1\n5 10\n2\n3 6",
"output": "70"
},
{
"input": "2\n3 8\n5 10\n1\n20",
"output": "74"
},
{
"input": "3\n10 3\n20 2\n30 1\n3\n30 50 60",
"output": "200"
},
{
"input": "1\n100 1000\n1\n1",
"output": "199000"
},
{
"input": "1\n1 1000\n1\n1",
"output": "1000"
},
{
"input": "1\n1 1000\n1\n2",
"output": "1000"
},
{
"input": "2\n1000000000 1000\n1 1\n1\n10",
"output": "1999999991001"
},
{
"input": "6\n5 9\n63 3\n30 4\n25 6\n48 2\n29 9\n8\n105 137 172 192 632 722 972 981",
"output": "2251"
},
{
"input": "7\n9902 9\n5809 6\n2358 0\n6868 7\n9630 2\n8302 10\n9422 3\n4\n2148 4563 8488 9575",
"output": "1481866"
},
{
"input": "9\n60129 6\n44235 10\n13131 8\n2012 2\n27536 4\n38950 6\n39080 2\n13892 3\n48709 0\n1\n23853",
"output": "2751752"
},
{
"input": "10\n3466127 4\n3477072 1\n9690039 9\n9885165 6\n2559197 4\n3448456 3\n9169542 1\n6915866 2\n1702896 10\n8934261 5\n6\n3041416 5811699 5920083 8250213 8694306 8899250",
"output": "1843409345"
},
{
"input": "4\n4059578 5\n20774712 1\n64867825 7\n5606945 8\n1\n337246111",
"output": "540002937"
},
{
"input": "16\n196661091 17\n765544213 322\n134522506 115\n914609421 163\n219016066 227\n835576807 856\n682158845 914\n11248128 145\n876496017 854\n141052597 530\n163180278 315\n407245991 60\n294673989 270\n2976249 26\n674132026 519\n347829904 23\n16\n6280951514 53396669509 79113951711 87247958777 121933859963 219062570855 250484361488 292915737777 357877371567 638447479028 646055798354 733144914116 746148995326 752707219571 888597178968 929325038582",
"output": "3493909415554"
},
{
"input": "12\n559720489 0\n961035680 0\n953017025 0\n333351645 0\n840947432 0\n265712969 0\n484023361 0\n215786741 0\n880533785 0\n678800187 0\n817395626 0\n591321601 0\n13\n2165448470 32644841954 456375244913 510187375384 524722185932 628130306204 701569710739 731515209935 745407119699 772031092452 783514111802 933457816308 991905864630",
"output": "0"
},
{
"input": "22\n2 103\n10 84\n7 834\n9 527\n3 415\n10 943\n1 633\n9 444\n7 639\n2 146\n9 208\n5 637\n4 1000\n4 606\n6 43\n2 437\n4 855\n1 70\n4 780\n8 214\n2 196\n1 261\n61\n2 3 6 9 11 12 13 16 17 19 21 24 26 29 31 33 35 36 38 39 40 42 44 46 49 52 53 54 56 59 61 64 66 67 70 72 75 77 78 80 83 84 87 90 92 93 95 98 100 102 105 107 109 112 114 115 116 117 120 122 125",
"output": "2004140"
},
{
"input": "14\n3 689\n4 4\n6 40\n10 309\n2 216\n5 575\n1 203\n5 216\n10 544\n7 979\n1 19\n1 876\n8 505\n4 217\n51\n1 4 5 8 12 18 20 22 26 30 33 39 43 46 50 52 57 59 63 68 73 74 78 79 82 85 90 96 100 104 109 113 118 119 122 126 130 136 138 140 144 147 149 150 156 157 163 164 169 174 178",
"output": "412722"
},
{
"input": "2\n3 116\n3 869\n80\n3 5 11 17 23 31 33 41 42 49 51 53 58 60 65 70 79 84 87 88 89 93 98 102 109 110 111 114 123 129 134 142 143 152 160 162 166 167 174 179 186 191 199 205 214 219 224 227 236 241 249 252 260 268 272 275 282 288 292 293 297 302 310 314 317 319 321 330 336 340 349 358 366 374 378 383 387 390 397 405",
"output": "6431"
},
{
"input": "20\n1 529\n15 864\n1 26\n7 582\n7 914\n4 535\n5 371\n15 500\n13 912\n1 354\n7 327\n7 470\n4 277\n20 656\n8 501\n8 419\n16 569\n2 587\n13 294\n11 37\n77\n1 3 6 8 9 11 12 13 14 16 18 20 22 24 27 30 33 34 35 36 38 40 43 44 46 49 52 54 56 57 60 63 64 66 68 70 73 74 75 77 78 79 80 81 84 86 89 92 93 95 96 97 99 101 103 106 109 111 112 114 115 118 119 120 121 122 123 124 125 128 130 133 134 137 139 140 142",
"output": "4860712"
},
{
"input": "20\n1 676\n10 2\n10 467\n7 826\n7 138\n8 76\n8 148\n2 121\n7 527\n3 571\n10 410\n7 174\n2 318\n6 97\n3 919\n8 684\n3 586\n4 570\n10 494\n8 582\n74\n1 6 10 15 20 22 25 26 27 29 32 33 34 37 39 44 49 52 53 55 56 61 65 66 70 72 74 77 79 80 83 85 88 91 95 98 103 106 107 112 114 119 124 129 133 137 138 140 144 146 147 149 153 155 157 160 165 168 172 173 177 180 181 184 188 193 198 201 206 208 209 213 216 218",
"output": "1497278"
},
{
"input": "1\n555 100\n10\n1 2 3 4 5 6 7 8 9 10",
"output": "605000"
},
{
"input": "1\n1 1\n1\n100000000000",
"output": "1"
},
{
"input": "12\n1000000000 1\n1000000000 2\n1000000000 3\n1000000000 4\n1000000000 5\n1000000000 6\n1000000000 7\n1000000000 8\n1000000000 9\n1000000000 10\n1000000000 11\n1000000000 12\n1\n10000000000",
"output": "101000000000"
},
{
"input": "11\n1000000000 1\n1000000000 2\n1000000000 3\n1000000000 4\n1000000000 5\n1000000000 6\n1000000000 7\n1000000000 8\n1000000000 9\n1000000000 10\n1000000000 11\n1\n10000000000",
"output": "77000000000"
},
{
"input": "1\n10 10\n3\n1 2 3",
"output": "340"
},
{
"input": "1\n1000000000 1000\n2\n3 6",
"output": "2999999991000"
},
{
"input": "1\n100 100\n3\n3 6 9",
"output": "38200"
},
{
"input": "1\n10 1\n10\n1 2 3 4 5 6 7 8 9 10",
"output": "55"
},
{
"input": "1\n10 10\n5\n1 2 3 4 5",
"output": "450"
},
{
"input": "10\n10 10\n10 10\n10 10\n10 10\n10 10\n10 10\n10 10\n10 10\n10 10\n10 10\n1\n1",
"output": "1990"
},
{
"input": "1\n10 10\n2\n3 6",
"output": "210"
},
{
"input": "10\n1000 1000\n1000 1000\n1000 1000\n1000 1000\n1000 1000\n1000 1000\n1000 1000\n1000 1000\n1000 1000\n1000 1000\n1\n1000000",
"output": "10000000"
}
] | 0 | 0 | -1 | 14,919 |
|
840 | Destiny | [
"data structures",
"probabilities"
] | null | null | Once, Leha found in the left pocket an array consisting of *n* integers, and in the right pocket *q* queries of the form *l* *r* *k*. If there are queries, then they must be answered. Answer for the query is minimal *x* such that *x* occurs in the interval *l* *r* strictly more than times or <=-<=1 if there is no such number. Help Leha with such a difficult task. | First line of input data contains two integers *n* and *q* (1<=≤<=*n*,<=*q*<=≤<=3·105) — number of elements in the array and number of queries respectively.
Next line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=*n*) — Leha's array.
Each of next *q* lines contains three integers *l*, *r* and *k* (1<=≤<=*l*<=≤<=*r*<=≤<=*n*,<=2<=≤<=*k*<=≤<=5) — description of the queries. | Output answer for each query in new line. | [
"4 2\n1 1 2 2\n1 3 2\n1 4 2\n",
"5 3\n1 2 1 3 2\n2 5 3\n1 2 3\n5 5 2\n"
] | [
"1\n-1\n",
"2\n1\n2\n"
] | none | [] | 2,500 | 213,299,200 | 0 | 14,925 |
|
980 | The Number Games | [
"data structures",
"greedy",
"trees"
] | null | null | The nation of Panel holds an annual show called The Number Games, where each district in the nation will be represented by one contestant.
The nation has $n$ districts numbered from $1$ to $n$, each district has exactly one path connecting it to every other district. The number of fans of a contestant from district $i$ is equal to $2^i$.
This year, the president decided to reduce the costs. He wants to remove $k$ contestants from the games. However, the districts of the removed contestants will be furious and will not allow anyone to cross through their districts.
The president wants to ensure that all remaining contestants are from districts that can be reached from one another. He also wishes to maximize the total number of fans of the participating contestants.
Which contestants should the president remove? | The first line of input contains two integers $n$ and $k$ ($1 \leq k < n \leq 10^6$) — the number of districts in Panel, and the number of contestants the president wishes to remove, respectively.
The next $n-1$ lines each contains two integers $a$ and $b$ ($1 \leq a, b \leq n$, $a \ne b$), that describe a road that connects two different districts $a$ and $b$ in the nation. It is guaranteed that there is exactly one path between every two districts. | Print $k$ space-separated integers: the numbers of the districts of which the contestants should be removed, in increasing order of district number. | [
"6 3\n2 1\n2 6\n4 2\n5 6\n2 3\n",
"8 4\n2 6\n2 7\n7 8\n1 2\n3 1\n2 4\n7 5\n"
] | [
"1 3 4\n",
"1 3 4 5\n"
] | In the first sample, the maximum possible total number of fans is $2^2 + 2^5 + 2^6 = 100$. We can achieve it by removing the contestants of the districts 1, 3, and 4. | [
{
"input": "6 3\n2 1\n2 6\n4 2\n5 6\n2 3",
"output": "1 3 4"
},
{
"input": "8 4\n2 6\n2 7\n7 8\n1 2\n3 1\n2 4\n7 5",
"output": "1 3 4 5"
},
{
"input": "2 1\n1 2",
"output": "1"
},
{
"input": "3 1\n2 1\n2 3",
"output": "1"
},
{
"input": "3 2\n1 3\n1 2",
"output": "1 2"
},
{
"input": "4 2\n4 2\n1 4\n3 2",
"output": "1 3"
},
{
"input": "15 3\n9 11\n11 8\n7 9\n9 14\n12 8\n10 7\n1 14\n1 5\n12 15\n10 3\n5 2\n13 15\n4 13\n6 4",
"output": "1 2 5"
},
{
"input": "15 12\n2 3\n2 14\n4 3\n4 10\n3 5\n1 4\n1 12\n4 15\n3 9\n10 7\n11 2\n12 8\n15 13\n1 6",
"output": "1 2 3 5 6 7 8 9 10 11 12 14"
},
{
"input": "32 16\n32 8\n11 32\n22 8\n22 17\n22 3\n16 22\n8 12\n22 7\n8 27\n11 6\n32 4\n9 8\n10 22\n22 31\n1 22\n21 11\n22 15\n14 32\n32 30\n22 29\n24 11\n18 11\n25 32\n13 8\n2 32\n28 8\n32 5\n11 20\n11 19\n22 23\n26 32",
"output": "1 2 3 4 5 6 7 9 10 12 13 14 15 16 17 18"
},
{
"input": "32 1\n30 25\n30 8\n8 22\n22 20\n21 20\n6 21\n29 6\n4 29\n2 4\n13 2\n1 13\n1 11\n11 24\n31 24\n31 15\n15 14\n27 14\n16 27\n5 16\n12 5\n9 12\n9 18\n3 18\n3 17\n17 19\n19 32\n32 10\n10 26\n7 26\n7 23\n23 28",
"output": "25"
},
{
"input": "32 2\n7 20\n15 20\n7 18\n31 20\n28 15\n20 25\n27 31\n27 6\n27 12\n6 16\n22 6\n21 22\n13 6\n16 5\n23 5\n23 26\n23 24\n23 17\n24 14\n17 4\n29 4\n2 24\n30 29\n1 29\n8 4\n30 32\n11 2\n32 3\n1 9\n11 10\n19 32",
"output": "3 8"
},
{
"input": "64 46\n52 22\n38 52\n28 38\n46 38\n30 38\n30 37\n7 37\n37 48\n48 27\n2 7\n27 11\n32 2\n32 35\n8 11\n59 32\n58 59\n59 24\n58 40\n40 4\n40 49\n40 41\n49 16\n9 16\n5 9\n12 9\n9 62\n3 62\n12 63\n63 25\n64 63\n63 42\n36 42\n45 36\n14 45\n53 45\n39 53\n60 39\n50 39\n50 23\n23 10\n19 50\n20 10\n19 56\n21 56\n31 56\n44 31\n26 31\n1 31\n43 44\n15 26\n15 6\n6 29\n47 6\n18 6\n29 55\n18 54\n33 54\n61 55\n54 17\n61 34\n13 17\n17 51\n57 34",
"output": "1 2 3 4 5 6 7 8 10 11 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 38 43 44 46 47 48 51 52 54 55 56 57 61"
},
{
"input": "64 63\n11 51\n64 11\n64 39\n11 6\n24 64\n51 63\n43 51\n64 29\n6 22\n47 6\n1 47\n41 22\n41 38\n4 47\n35 47\n41 23\n45 1\n52 35\n26 45\n15 35\n21 35\n23 32\n12 21\n21 62\n25 21\n28 25\n15 54\n57 12\n20 28\n48 57\n8 57\n20 44\n46 28\n18 57\n8 9\n27 9\n48 34\n50 46\n9 56\n9 61\n7 56\n19 61\n61 17\n42 17\n19 58\n58 30\n7 14\n7 59\n31 19\n17 5\n55 14\n13 31\n2 31\n59 40\n55 49\n2 60\n2 53\n36 2\n37 13\n2 16\n53 33\n37 10\n60 3",
"output": "1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63"
},
{
"input": "64 21\n33 48\n33 64\n55 48\n11 55\n18 11\n62 55\n48 57\n17 62\n64 52\n30 48\n49 48\n23 18\n13 11\n9 64\n11 5\n11 45\n2 55\n62 56\n64 36\n33 10\n34 18\n55 43\n3 48\n60 62\n48 32\n33 8\n62 41\n44 11\n33 46\n15 33\n14 62\n11 6\n64 31\n62 20\n64 25\n62 51\n53 33\n62 40\n18 4\n16 62\n21 11\n33 22\n37 33\n59 62\n55 7\n27 64\n24 64\n39 64\n19 62\n54 55\n33 61\n47 48\n58 55\n42 55\n38 11\n50 18\n28 48\n11 26\n11 1\n62 35\n64 29\n12 33\n18 63",
"output": "1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 19 20 21 22 23"
}
] | 0 | 0 | -1 | 14,954 |
|
138 | Hellish Constraints | [
"brute force",
"dp",
"two pointers"
] | null | null | Katya recently started to invent programming tasks and prepare her own contests. What she does not like is boring and simple constraints. Katya is fed up with all those "*N* does not exceed a thousand" and "the sum of *a**i* does not exceed a million" and she decided to come up with something a little more complicated.
The last problem written by Katya deals with strings. The input is a string of small Latin letters. To make the statement longer and strike terror into the people who will solve the contest, Katya came up with the following set of *k* restrictions of the same type (characters in restrictions can be repeated and some restrictions may contradict each other):
- The number of characters *c*1 in a string is not less than *l*1 and not more than *r*1. - ... - The number of characters *c**i* in a string is not less than *l**i* and not more than *r**i*. - ... - The number of characters *c**k* in a string is not less than *l**k* and not more than *r**k*.
However, having decided that it is too simple and obvious, Katya added the following condition: a string meets no less than *L* and not more than *R* constraints from the above given list.
Katya does not like to compose difficult and mean tests, so she just took a big string *s* and wants to add to the tests all its substrings that meet the constraints. However, Katya got lost in her conditions and asked you to count the number of substrings of the string *s* that meet the conditions (each occurrence of the substring is counted separately). | The first line contains a non-empty string *s*, consisting of small Latin letters. The length of the string *s* does not exceed 105.
The second line contains three space-separated integers *k*, *L* and *R* (0<=≤<=*L*<=≤<=*R*<=≤<=*k*<=≤<=500).
Next *k* lines contain Katya's constrictions in the following form "*c**i* *l**i* *r**i*". All letters *c**i* are small Latin letters, *l**i* and *r**i* are integers (0<=≤<=*l**i*<=≤<=*r**i*<=≤<=|*s*|, where |*s*| is the length of string *s*). Letters *c**i* are not necessarily different. | Print a single number — the number of substrings that meet the constrictions.
Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cout stream or the %I64d specificator. | [
"codeforces\n2 0 0\no 1 2\ne 1 2\n",
"codeforces\n2 1 1\no 1 2\no 1 2\n"
] | [
"7\n",
"0\n"
] | In the first test we should count the number of strings that do not contain characters "e" and "o". All such strings are as follows (in the order of occurrence in the initial string from the left to the right): "c", "d"', "f", "r", "rc", "c", "s".
In the second test we cannot achieve fulfilling exactly one of the two identical constrictions, so the answer is 0. | [] | 186 | 2,252,800 | -1 | 14,988 |
|
547 | Mike and Foam | [
"bitmasks",
"combinatorics",
"dp",
"math",
"number theory"
] | null | null | Mike is a bartender at Rico's bar. At Rico's, they put beer glasses in a special shelf. There are *n* kinds of beer at Rico's numbered from 1 to *n*. *i*-th kind of beer has *a**i* milliliters of foam on it.
Maxim is Mike's boss. Today he told Mike to perform *q* queries. Initially the shelf is empty. In each request, Maxim gives him a number *x*. If beer number *x* is already in the shelf, then Mike should remove it from the shelf, otherwise he should put it in the shelf.
After each query, Mike should tell him the score of the shelf. Bears are geeks. So they think that the score of a shelf is the number of pairs (*i*,<=*j*) of glasses in the shelf such that *i*<=<<=*j* and where is the greatest common divisor of numbers *a* and *b*.
Mike is tired. So he asked you to help him in performing these requests. | The first line of input contains numbers *n* and *q* (1<=≤<=*n*,<=*q*<=≤<=2<=×<=105), the number of different kinds of beer and number of queries.
The next line contains *n* space separated integers, *a*1,<=*a*2,<=... ,<=*a**n* (1<=≤<=*a**i*<=≤<=5<=×<=105), the height of foam in top of each kind of beer.
The next *q* lines contain the queries. Each query consists of a single integer integer *x* (1<=≤<=*x*<=≤<=*n*), the index of a beer that should be added or removed from the shelf. | For each query, print the answer for that query in one line. | [
"5 6\n1 2 3 4 6\n1\n2\n3\n4\n5\n1\n"
] | [
"0\n1\n3\n5\n6\n2\n"
] | none | [
{
"input": "5 6\n1 2 3 4 6\n1\n2\n3\n4\n5\n1",
"output": "0\n1\n3\n5\n6\n2"
},
{
"input": "3 3\n151790 360570 1\n2\n3\n3",
"output": "0\n1\n0"
},
{
"input": "1 1\n1\n1",
"output": "0"
},
{
"input": "5 10\n1 1 1 1 1\n1\n2\n3\n4\n5\n5\n4\n3\n2\n1",
"output": "0\n1\n3\n6\n10\n6\n3\n1\n0\n0"
},
{
"input": "1 2\n499590\n1\n1",
"output": "0\n0"
}
] | 2,000 | 14,745,600 | 0 | 14,999 |
|
472 | Design Tutorial: Learn from Life | [] | null | null | One way to create a task is to learn from life. You can choose some experience in real life, formalize it and then you will get a new task.
Let's think about a scene in real life: there are lots of people waiting in front of the elevator, each person wants to go to a certain floor. We can formalize it in the following way. We have *n* people standing on the first floor, the *i*-th person wants to go to the *f**i*-th floor. Unfortunately, there is only one elevator and its capacity equal to *k* (that is at most *k* people can use it simultaneously). Initially the elevator is located on the first floor. The elevator needs |*a*<=-<=*b*| seconds to move from the *a*-th floor to the *b*-th floor (we don't count the time the people need to get on and off the elevator).
What is the minimal number of seconds that is needed to transport all the people to the corresponding floors and then return the elevator to the first floor? | The first line contains two integers *n* and *k* (1<=≤<=*n*,<=*k*<=≤<=2000) — the number of people and the maximal capacity of the elevator.
The next line contains *n* integers: *f*1,<=*f*2,<=...,<=*f**n* (2<=≤<=*f**i*<=≤<=2000), where *f**i* denotes the target floor of the *i*-th person. | Output a single integer — the minimal time needed to achieve the goal. | [
"3 2\n2 3 4\n",
"4 2\n50 100 50 100\n",
"10 3\n2 2 2 2 2 2 2 2 2 2\n"
] | [
"8\n",
"296\n",
"8\n"
] | In first sample, an optimal solution is:
1. The elevator takes up person #1 and person #2. 1. It goes to the 2nd floor. 1. Both people go out of the elevator. 1. The elevator goes back to the 1st floor. 1. Then the elevator takes up person #3. 1. And it goes to the 2nd floor. 1. It picks up person #2. 1. Then it goes to the 3rd floor. 1. Person #2 goes out. 1. Then it goes to the 4th floor, where person #3 goes out. 1. The elevator goes back to the 1st floor. | [
{
"input": "3 2\n2 3 4",
"output": "8"
},
{
"input": "4 2\n50 100 50 100",
"output": "296"
},
{
"input": "10 3\n2 2 2 2 2 2 2 2 2 2",
"output": "8"
},
{
"input": "1 1\n2",
"output": "2"
},
{
"input": "2 1\n2 2",
"output": "4"
},
{
"input": "2 2\n2 2",
"output": "2"
},
{
"input": "11 4\n2 3 4 5 6 7 8 9 10 11 12",
"output": "42"
},
{
"input": "70 1311\n1146 769 1530 1132 877 1352 1295 1282 1086 914 852 1351 1432 847 1105 776 1278 716 1435 749 1320 869 812 1179 1239 1426 1403 1296 1489 1018 848 1215 1278 1203 1386 1113 812 896 1287 733 1328 1517 964 1317 1487 1322 1281 843 863 1220 790 1121 1442 726 957 1465 974 1314 993 1286 1163 938 902 1197 859 807 718 916 783 1450",
"output": "3058"
},
{
"input": "22 1481\n1555 1499 1615 535 399 795 432 1830 1645 452 278 1173 1501 1779 317 796 1855 1631 651 495 236 1122",
"output": "3708"
},
{
"input": "100 1\n100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100",
"output": "19800"
},
{
"input": "100 100\n100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100",
"output": "198"
},
{
"input": "2 1\n2000 2000",
"output": "7996"
},
{
"input": "5 3\n2000 2000 2000 2000 1999",
"output": "7996"
}
] | 62 | 1,536,000 | 3 | 15,003 |
|
989 | A Shade of Moonlight | [
"binary search",
"geometry",
"math",
"sortings",
"two pointers"
] | null | null | "To curtain off the moonlight should be hardly possible; the shades present its mellow beauty and restful nature." Intonates Mino.
"See? The clouds are coming." Kanno gazes into the distance.
"That can't be better," Mino turns to Kanno.
The sky can be seen as a one-dimensional axis. The moon is at the origin whose coordinate is $0$.
There are $n$ clouds floating in the sky. Each cloud has the same length $l$. The $i$-th initially covers the range of $(x_i, x_i + l)$ (endpoints excluded). Initially, it moves at a velocity of $v_i$, which equals either $1$ or $-1$.
Furthermore, no pair of clouds intersect initially, that is, for all $1 \leq i \lt j \leq n$, $\lvert x_i - x_j \rvert \geq l$.
With a wind velocity of $w$, the velocity of the $i$-th cloud becomes $v_i + w$. That is, its coordinate increases by $v_i + w$ during each unit of time. Note that the wind can be strong and clouds can change their direction.
You are to help Mino count the number of pairs $(i, j)$ ($i < j$), such that with a proper choice of wind velocity $w$ not exceeding $w_\mathrm{max}$ in absolute value (possibly negative and/or fractional), the $i$-th and $j$-th clouds both cover the moon at the same future moment. This $w$ doesn't need to be the same across different pairs. | The first line contains three space-separated integers $n$, $l$, and $w_\mathrm{max}$ ($1 \leq n \leq 10^5$, $1 \leq l, w_\mathrm{max} \leq 10^8$) — the number of clouds, the length of each cloud and the maximum wind speed, respectively.
The $i$-th of the following $n$ lines contains two space-separated integers $x_i$ and $v_i$ ($-10^8 \leq x_i \leq 10^8$, $v_i \in \{-1, 1\}$) — the initial position and the velocity of the $i$-th cloud, respectively.
The input guarantees that for all $1 \leq i \lt j \leq n$, $\lvert x_i - x_j \rvert \geq l$. | Output one integer — the number of unordered pairs of clouds such that it's possible that clouds from each pair cover the moon at the same future moment with a proper choice of wind velocity $w$. | [
"5 1 2\n-2 1\n2 1\n3 -1\n5 -1\n7 -1\n",
"4 10 1\n-20 1\n-10 -1\n0 1\n10 -1\n"
] | [
"4\n",
"1\n"
] | In the first example, the initial positions and velocities of clouds are illustrated below.
The pairs are:
- $(1, 3)$, covering the moon at time $2.5$ with $w = -0.4$; - $(1, 4)$, covering the moon at time $3.5$ with $w = -0.6$; - $(1, 5)$, covering the moon at time $4.5$ with $w = -0.7$; - $(2, 5)$, covering the moon at time $2.5$ with $w = -2$.
Below is the positions of clouds at time $2.5$ with $w = -0.4$. At this moment, the $1$-st and $3$-rd clouds both cover the moon.
In the second example, the only pair is $(1, 4)$, covering the moon at time $15$ with $w = 0$.
Note that all the times and wind velocities given above are just examples among infinitely many choices. | [
{
"input": "5 1 2\n-2 1\n2 1\n3 -1\n5 -1\n7 -1",
"output": "4"
},
{
"input": "4 10 1\n-20 1\n-10 -1\n0 1\n10 -1",
"output": "1"
},
{
"input": "1 100000000 98765432\n73740702 1",
"output": "0"
},
{
"input": "10 2 3\n-1 -1\n-4 1\n-6 -1\n1 1\n10 -1\n-8 -1\n6 1\n8 1\n4 -1\n-10 -1",
"output": "5"
},
{
"input": "3 100000000 100000000\n-100000000 1\n100000000 1\n0 -1",
"output": "1"
},
{
"input": "9 25000000 989\n-100000000 -1\n-75000000 1\n75000000 1\n50000000 -1\n-50000000 1\n0 1\n25000000 1\n-25000000 -1\n100000000 -1",
"output": "11"
},
{
"input": "2 5 1\n-2 1\n5 -1",
"output": "1"
},
{
"input": "2 5 1\n-9 -1\n-2 1",
"output": "0"
},
{
"input": "3 4 5\n9 1\n-4 1\n-8 -1",
"output": "0"
},
{
"input": "5 1 1\n-6 1\n15 1\n-7 1\n-13 -1\n12 -1",
"output": "2"
},
{
"input": "50 1 19\n-5213 -1\n2021 -1\n-4479 1\n1569 -1\n1618 1\n-8318 1\n3854 1\n8190 -1\n9162 1\n8849 1\n-5545 -1\n-7898 -1\n728 1\n-2175 -1\n6453 -1\n2999 1\n4716 1\n-2192 -1\n7938 -1\n1910 -1\n-6863 -1\n5230 -1\n-2782 -1\n-2587 -1\n-3389 1\n-332 -1\n5915 1\n-2604 1\n-8907 1\n-2019 1\n2992 1\n-3279 -1\n6720 1\n4332 1\n8789 -1\n2003 1\n-8046 -1\n-594 -1\n-4133 -1\n-7954 -1\n-6270 -1\n4042 -1\n3650 1\n-8569 1\n2529 -1\n266 -1\n3405 -1\n-9753 1\n1205 -1\n6437 -1",
"output": "262"
},
{
"input": "50 100 40\n4843 -1\n7653 1\n5391 1\n-1651 1\n-8530 -1\n9770 1\n2721 1\n7321 1\n-3636 -1\n-1525 -1\n-3060 1\n1877 -1\n3771 -1\n-7651 1\n581 -1\n1127 -1\n6966 -1\n-6089 1\n1465 -1\n3147 -1\n-6927 -1\n4477 1\n-6535 1\n5991 -1\n-2740 1\n5021 1\n-7761 -1\n4626 1\n9958 1\n4275 1\n5695 1\n8835 -1\n7791 -1\n189 -1\n-170 1\n-4468 -1\n-708 1\n34 -1\n-9068 1\n6424 -1\n-2066 -1\n-7367 1\n6224 1\n3329 1\n-1809 -1\n7105 1\n-4607 -1\n-3174 -1\n-9782 -1\n1350 -1",
"output": "253"
}
] | 1,044 | 8,806,400 | 0 | 15,053 |
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