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codeforces-problems

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problem_statement stringlengths 147 8.53k	input stringlengths 1 771	output stringlengths 1 592 ⌀	time_limit stringclasses 32 values	memory_limit stringclasses 21 values	tags stringlengths 6 168
C. k-Treetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputQuite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a k-tree.A k-tree is an infinite rooted tree where: each vertex has exactly k children; each edge has some weight; if we look at the edges that goes from some vertex to its children (exactly k edges), then their weights will equal 1, 2, 3, ..., k. The picture below shows a part of a 3-tree. As soon as Dima, a good friend of Lesha, found out about the tree, he immediately wondered: "How many paths of total weight n (the sum of all weights of the edges in the path) are there, starting from the root of a k-tree and also containing at least one edge of weight at least d?".Help Dima find an answer to his question. As the number of ways can be rather large, print it modulo 1000000007 (109 + 7). InputA single line contains three space-separated integers: n, k and d (1 ≤ n, k ≤ 100; 1 ≤ d ≤ k).OutputPrint a single integer — the answer to the problem modulo 1000000007 (109 + 7). ExamplesInput3 3 2Output3Input3 3 3Output1Input4 3 2Output6Input4 5 2Output7	Input3 3 2	Output3	1 second	256 megabytes	['dp', 'implementation', 'trees', '*1600']
B. Shower Linetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputMany students live in a dormitory. A dormitory is a whole new world of funny amusements and possibilities but it does have its drawbacks. There is only one shower and there are multiple students who wish to have a shower in the morning. That's why every morning there is a line of five people in front of the dormitory shower door. As soon as the shower opens, the first person from the line enters the shower. After a while the first person leaves the shower and the next person enters the shower. The process continues until everybody in the line has a shower.Having a shower takes some time, so the students in the line talk as they wait. At each moment of time the students talk in pairs: the (2i - 1)-th man in the line (for the current moment) talks with the (2i)-th one. Let's look at this process in more detail. Let's number the people from 1 to 5. Let's assume that the line initially looks as 23154 (person number 2 stands at the beginning of the line). Then, before the shower opens, 2 talks with 3, 1 talks with 5, 4 doesn't talk with anyone. Then 2 enters the shower. While 2 has a shower, 3 and 1 talk, 5 and 4 talk too. Then, 3 enters the shower. While 3 has a shower, 1 and 5 talk, 4 doesn't talk to anyone. Then 1 enters the shower and while he is there, 5 and 4 talk. Then 5 enters the shower, and then 4 enters the shower.We know that if students i and j talk, then the i-th student's happiness increases by gij and the j-th student's happiness increases by gji. Your task is to find such initial order of students in the line that the total happiness of all students will be maximum in the end. Please note that some pair of students may have a talk several times. In the example above students 1 and 5 talk while they wait for the shower to open and while 3 has a shower.InputThe input consists of five lines, each line contains five space-separated integers: the j-th number in the i-th line shows gij (0 ≤ gij ≤ 105). It is guaranteed that gii = 0 for all i.Assume that the students are numbered from 1 to 5.OutputPrint a single integer — the maximum possible total happiness of the students.ExamplesInput0 0 0 0 90 0 0 0 00 0 0 0 00 0 0 0 07 0 0 0 0Output32Input0 43 21 18 23 0 21 11 655 2 0 1 454 62 12 0 9987 64 81 33 0Output620NoteIn the first sample, the optimal arrangement of the line is 23154. In this case, the total happiness equals:(g23 + g32 + g15 + g51) + (g13 + g31 + g54 + g45) + (g15 + g51) + (g54 + g45) = 32.	Input0 0 0 0 90 0 0 0 00 0 0 0 00 0 0 0 07 0 0 0 0	Output32	1 second	256 megabytes	['brute force', 'implementation', '*1200']
A. Black Squaretime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputQuite recently, a very smart student named Jury decided that lectures are boring, so he downloaded a game called "Black Square" on his super cool touchscreen phone.In this game, the phone's screen is divided into four vertical strips. Each second, a black square appears on some of the strips. According to the rules of the game, Jury must use this second to touch the corresponding strip to make the square go away. As Jury is both smart and lazy, he counted that he wastes exactly ai calories on touching the i-th strip.You've got a string s, describing the process of the game and numbers a1, a2, a3, a4. Calculate how many calories Jury needs to destroy all the squares?InputThe first line contains four space-separated integers a1, a2, a3, a4 (0 ≤ a1, a2, a3, a4 ≤ 104).The second line contains string s (1 ≤ \|s\| ≤ 105), where the і-th character of the string equals "1", if on the i-th second of the game the square appears on the first strip, "2", if it appears on the second strip, "3", if it appears on the third strip, "4", if it appears on the fourth strip.OutputPrint a single integer — the total number of calories that Jury wastes.ExamplesInput1 2 3 4123214Output13Input1 5 3 211221Output13	Input1 2 3 4123214	Output13	1 second	256 megabytes	['implementation', '*800']
B. Balls Gametime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIahub is training for the IOI. What is a better way to train than playing a Zuma-like game? There are n balls put in a row. Each ball is colored in one of k colors. Initially the row doesn't contain three or more contiguous balls with the same color. Iahub has a single ball of color x. He can insert his ball at any position in the row (probably, between two other balls). If at any moment there are three or more contiguous balls of the same color in the row, they are destroyed immediately. This rule is applied multiple times, until there are no more sets of 3 or more contiguous balls of the same color. For example, if Iahub has the row of balls [black, black, white, white, black, black] and a white ball, he can insert the ball between two white balls. Thus three white balls are destroyed, and then four black balls become contiguous, so all four balls are destroyed. The row will not contain any ball in the end, so Iahub can destroy all 6 balls.Iahub wants to destroy as many balls as possible. You are given the description of the row of balls, and the color of Iahub's ball. Help Iahub train for the IOI by telling him the maximum number of balls from the row he can destroy.InputThe first line of input contains three integers: n (1 ≤ n ≤ 100), k (1 ≤ k ≤ 100) and x (1 ≤ x ≤ k). The next line contains n space-separated integers c1, c2, ..., cn (1 ≤ ci ≤ k). Number ci means that the i-th ball in the row has color ci.It is guaranteed that the initial row of balls will never contain three or more contiguous balls of the same color. OutputPrint a single integer — the maximum number of balls Iahub can destroy.ExamplesInput6 2 21 1 2 2 1 1Output6Input1 1 11Output0	Input6 2 21 1 2 2 1 1	Output6	1 second	256 megabytes	['brute force', 'two pointers', '*1400']
A. Points and Segments (easy)time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIahub isn't well prepared on geometry problems, but he heard that this year there will be a lot of geometry problems on the IOI selection camp. Scared, Iahub locked himself in the basement and started thinking of new problems of this kind. One of them is the following.Iahub wants to draw n distinct points and m segments on the OX axis. He can draw each point with either red or blue. The drawing is good if and only if the following requirement is met: for each segment [li, ri] consider all the red points belong to it (ri points), and all the blue points belong to it (bi points); each segment i should satisfy the inequality \|ri - bi\| ≤ 1.Iahub thinks that point x belongs to segment [l, r], if inequality l ≤ x ≤ r holds.Iahub gives to you all coordinates of points and segments. Please, help him to find any good drawing.InputThe first line of input contains two integers: n (1 ≤ n ≤ 100) and m (1 ≤ m ≤ 100). The next line contains n space-separated integers x1, x2, ..., xn (0 ≤ xi ≤ 100) — the coordinates of the points. The following m lines contain the descriptions of the m segments. Each line contains two integers li and ri (0 ≤ li ≤ ri ≤ 100) — the borders of the i-th segment.It's guaranteed that all the points are distinct.OutputIf there is no good drawing for a given test, output a single integer -1. Otherwise output n integers, each integer must be 0 or 1. The i-th number denotes the color of the i-th point (0 is red, and 1 is blue).If there are multiple good drawings you can output any of them.ExamplesInput3 33 7 141 56 1011 15Output0 0 0Input3 41 2 31 22 35 62 2Output1 0 1	Input3 33 7 141 56 1011 15	Output0 0 0	1 second	256 megabytes	['constructive algorithms', 'sortings', '*1600']
E. Points and Segmentstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIahub isn't well prepared on geometry problems, but he heard that this year there will be a lot of geometry problems on the IOI selection camp. Scared, Iahub locked himself in the basement and started thinking of new problems of this kind. One of them is the following.Iahub wants to draw n distinct segments [li, ri] on the OX axis. He can draw each segment with either red or blue. The drawing is good if and only if the following requirement is met: for each point x of the OX axis consider all the segments that contains point x; suppose, that rx red segments and bx blue segments contain point x; for each point x inequality \|rx - bx\| ≤ 1 must be satisfied.A segment [l, r] contains a point x if and only if l ≤ x ≤ r.Iahub gives you the starting and ending points of all the segments. You have to find any good drawing for him.InputThe first line of input contains integer n (1 ≤ n ≤ 105) — the number of segments. The i-th of the next n lines contains two integers li and ri (0 ≤ li ≤ ri ≤ 109) — the borders of the i-th segment.It's guaranteed that all the segments are distinct.OutputIf there is no good drawing for a given test, output a single integer -1. Otherwise output n integers; each integer must be 0 or 1. The i-th number denotes the color of the i-th segment (0 is red and 1 is blue).If there are multiple good drawings you can output any of them.ExamplesInput20 22 3Output0 1Input61 51 33 52 1011 1112 12Output0 1 0 1 0 0	Input20 22 3	Output0 1	1 second	256 megabytes	['graphs', '*3000']
D. Tricky Functiontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputIahub and Sorin are the best competitive programmers in their town. However, they can't both qualify to an important contest. The selection will be made with the help of a single problem. Blatnatalag, a friend of Iahub, managed to get hold of the problem before the contest. Because he wants to make sure Iahub will be the one qualified, he tells Iahub the following task.You're given an (1-based) array a with n elements. Let's define function f(i, j) (1 ≤ i, j ≤ n) as (i - j)2 + g(i, j)2. Function g is calculated by the following pseudo-code:int g(int i, int j) { int sum = 0; for (int k = min(i, j) + 1; k <= max(i, j); k = k + 1) sum = sum + a[k]; return sum;}Find a value mini ≠ j f(i, j).Probably by now Iahub already figured out the solution to this problem. Can you?InputThe first line of input contains a single integer n (2 ≤ n ≤ 100000). Next line contains n integers a[1], a[2], ..., a[n] ( - 104 ≤ a[i] ≤ 104). OutputOutput a single integer — the value of mini ≠ j f(i, j).ExamplesInput41 0 0 -1Output1Input21 -1Output2	Input41 0 0 -1	Output1	2 seconds	256 megabytes	['data structures', 'divide and conquer', 'geometry', '*2200']
C. Guess the Treetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. Iahub asks Iahubina: can you build a rooted tree, such that each internal node (a node with at least one son) has at least two sons; node i has ci nodes in its subtree? Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.InputThe first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents ci (1 ≤ ci ≤ n).OutputOutput on the first line "YES" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output "NO" (without quotes). ExamplesInput41 1 1 4OutputYESInput51 1 5 2 1OutputNO	Input41 1 1 4	OutputYES	1 second	256 megabytes	['bitmasks', 'constructive algorithms', 'dp', 'greedy', 'trees', '*2300']
B. Working outtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputSummer is coming! It's time for Iahub and Iahubina to work out, as they both want to look hot at the beach. The gym where they go is a matrix a with n lines and m columns. Let number a[i][j] represents the calories burned by performing workout at the cell of gym in the i-th line and the j-th column.Iahub starts with workout located at line 1 and column 1. He needs to finish with workout a[n][m]. After finishing workout a[i][j], he can go to workout a[i + 1][j] or a[i][j + 1]. Similarly, Iahubina starts with workout a[n][1] and she needs to finish with workout a[1][m]. After finishing workout from cell a[i][j], she goes to either a[i][j + 1] or a[i - 1][j]. There is one additional condition for their training. They have to meet in exactly one cell of gym. At that cell, none of them will work out. They will talk about fast exponentiation (pretty odd small talk) and then both of them will move to the next workout.If a workout was done by either Iahub or Iahubina, it counts as total gain. Please plan a workout for Iahub and Iahubina such as total gain to be as big as possible. Note, that Iahub and Iahubina can perform workouts with different speed, so the number of cells that they use to reach meet cell may differs.InputThe first line of the input contains two integers n and m (3 ≤ n, m ≤ 1000). Each of the next n lines contains m integers: j-th number from i-th line denotes element a[i][j] (0 ≤ a[i][j] ≤ 105).OutputThe output contains a single number — the maximum total gain possible. ExamplesInput3 3100 100 100100 1 100100 100 100Output800NoteIahub will choose exercises a[1][1] → a[1][2] → a[2][2] → a[3][2] → a[3][3]. Iahubina will choose exercises a[3][1] → a[2][1] → a[2][2] → a[2][3] → a[1][3].	Input3 3100 100 100100 1 100100 100 100	Output800	2 seconds	256 megabytes	['dp', '*1600']
A. Xor-treetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIahub is very proud of his recent discovery, propagating trees. Right now, he invented a new tree, called xor-tree. After this new revolutionary discovery, he invented a game for kids which uses xor-trees.The game is played on a tree having n nodes, numbered from 1 to n. Each node i has an initial value initi, which is either 0 or 1. The root of the tree is node 1.One can perform several (possibly, zero) operations on the tree during the game. The only available type of operation is to pick a node x. Right after someone has picked node x, the value of node x flips, the values of sons of x remain the same, the values of sons of sons of x flips, the values of sons of sons of sons of x remain the same and so on.The goal of the game is to get each node i to have value goali, which can also be only 0 or 1. You need to reach the goal of the game by using minimum number of operations.InputThe first line contains an integer n (1 ≤ n ≤ 105). Each of the next n - 1 lines contains two integers ui and vi (1 ≤ ui, vi ≤ n; ui ≠ vi) meaning there is an edge between nodes ui and vi. The next line contains n integer numbers, the i-th of them corresponds to initi (initi is either 0 or 1). The following line also contains n integer numbers, the i-th number corresponds to goali (goali is either 0 or 1).OutputIn the first line output an integer number cnt, representing the minimal number of operations you perform. Each of the next cnt lines should contain an integer xi, representing that you pick a node xi.ExamplesInput102 13 14 25 16 27 58 69 810 51 0 1 1 0 1 0 1 0 11 0 1 0 0 1 1 1 0 1Output247	Input102 13 14 25 16 27 58 69 810 51 0 1 1 0 1 0 1 0 11 0 1 0 0 1 1 1 0 1	Output247	1 second	256 megabytes	['dfs and similar', 'trees', '*1300']
E. Police Patroltime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputImagine that your city is an infinite 2D plane with Cartesian coordinate system. The only crime-affected road of your city is the x-axis. Currently, there are n criminals along the road. No police station has been built on this road yet, so the mayor wants to build one.As you are going to be in charge of this new police station, the mayor has asked you to choose a suitable position (some integer point) for building it. You should choose the best position for the police station, so that you could minimize the total time of your criminal catching mission. Your mission of catching the criminals will operate only from this station. The new station will have only one patrol car. You will go to the criminals by this car, carry them on the car, bring them back to the police station and put them in prison. The patrol car can carry at most m criminals at a time. Note that, the criminals don't know about your mission. So, they will stay where they are instead of running away.Your task is to find the position for the police station, so that total distance you need to cover to catch all the criminals will be minimum possible. Note that, you also can built the police station on the positions where one or more criminals already exist. In such a case all these criminals are arrested instantly.InputThe first line of the input will have two integers n (1 ≤ n ≤ 106) and m (1 ≤ m ≤ 106) separated by spaces. The next line will contain n integers separated by spaces. The ith integer is the position of the ith criminal on the x-axis. Absolute value of positions will not exceed 109. If a criminal has position x, he/she is located in the point (x, 0) of the plane. The positions of the criminals will be given in non-decreasing order. Note, that there can be more than one criminal standing at some point of the plane.Note: since the size of the input/output could be very large, don't use slow input/output techniques in your language. For example, do not use input/output streams (cin, cout) in C++.OutputPrint a single integer, that means the minimum possible distance you need to cover to catch all the criminals.ExamplesInput3 61 2 3Output4Input5 5-7 -6 -3 -1 1Output16Input1 3690Output0Input11 2-375 -108 1336 1453 1598 1892 2804 3732 4291 4588 4822Output18716	Input3 61 2 3	Output4	1 second	256 megabytes	['greedy', 'implementation', 'math', 'ternary search', '*2000']
D. Match & Catchtime limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard outputPolice headquarter is monitoring signal on different frequency levels. They have got two suspiciously encoded strings s1 and s2 from two different frequencies as signals. They are suspecting that these two strings are from two different criminals and they are planning to do some evil task.Now they are trying to find a common substring of minimum length between these two strings. The substring must occur only once in the first string, and also it must occur only once in the second string.Given two strings s1 and s2 consist of lowercase Latin letters, find the smallest (by length) common substring p of both s1 and s2, where p is a unique substring in s1 and also in s2. See notes for formal definition of substring and uniqueness.InputThe first line of input contains s1 and the second line contains s2 (1 ≤ \|s1\|, \|s2\| ≤ 5000). Both strings consist of lowercase Latin letters.OutputPrint the length of the smallest common unique substring of s1 and s2. If there are no common unique substrings of s1 and s2 print -1.ExamplesInputapplepepperoniOutput2InputloverdriverOutput1InputbidhanroyOutput-1InputtestsetsesteeptesOutput3NoteImagine we have string a = a1a2a3...a\|a\|, where \|a\| is the length of string a, and ai is the ith letter of the string. We will call string alal + 1al + 2...ar (1 ≤ l ≤ r ≤ \|a\|) the substring [l, r] of the string a. The substring [l, r] is unique in a if and only if there is no pair l1, r1 such that l1 ≠ l and the substring [l1, r1] is equal to the substring [l, r] in a.	Inputapplepepperoni	Output2	1 second	512 megabytes	['dp', 'string suffix structures', 'strings', '*2200']
C. Checkpoststime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYour city has n junctions. There are m one-way roads between the junctions. As a mayor of the city, you have to ensure the security of all the junctions.To ensure the security, you have to build some police checkposts. Checkposts can only be built in a junction. A checkpost at junction i can protect junction j if either i = j or the police patrol car can go to j from i and then come back to i.Building checkposts costs some money. As some areas of the city are more expensive than others, building checkpost at some junctions might cost more money than other junctions.You have to determine the minimum possible money needed to ensure the security of all the junctions. Also you have to find the number of ways to ensure the security in minimum price and in addition in minimum number of checkposts. Two ways are different if any of the junctions contains a checkpost in one of them and do not contain in the other.InputIn the first line, you will be given an integer n, number of junctions (1 ≤ n ≤ 105). In the next line, n space-separated integers will be given. The ith integer is the cost of building checkpost at the ith junction (costs will be non-negative and will not exceed 109).The next line will contain an integer m (0 ≤ m ≤ 3·105). And each of the next m lines contains two integers ui and vi (1 ≤ ui, vi ≤ n; u ≠ v). A pair ui, vi means, that there is a one-way road which goes from ui to vi. There will not be more than one road between two nodes in the same direction.OutputPrint two integers separated by spaces. The first one is the minimum possible money needed to ensure the security of all the junctions. And the second one is the number of ways you can ensure the security modulo 1000000007 (109 + 7).ExamplesInput31 2 331 22 33 2Output3 1Input52 8 0 6 061 41 32 43 44 55 1Output8 2Input101 3 2 2 1 3 1 4 10 10121 22 33 13 44 55 65 76 47 38 99 1010 9Output15 6Input27 9121 22 1Output7 1	Input31 2 331 22 33 2	Output3 1	2 seconds	256 megabytes	['dfs and similar', 'graphs', 'two pointers', '*1700']
B. Prison Transfertime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe prison of your city has n prisoners. As the prison can't accommodate all of them, the city mayor has decided to transfer c of the prisoners to a prison located in another city.For this reason, he made the n prisoners to stand in a line, with a number written on their chests. The number is the severity of the crime he/she has committed. The greater the number, the more severe his/her crime was.Then, the mayor told you to choose the c prisoners, who will be transferred to the other prison. He also imposed two conditions. They are, The chosen c prisoners has to form a contiguous segment of prisoners. Any of the chosen prisoner's crime level should not be greater then t. Because, that will make the prisoner a severe criminal and the mayor doesn't want to take the risk of his running away during the transfer. Find the number of ways you can choose the c prisoners.InputThe first line of input will contain three space separated integers n (1 ≤ n ≤ 2·105), t (0 ≤ t ≤ 109) and c (1 ≤ c ≤ n). The next line will contain n space separated integers, the ith integer is the severity ith prisoner's crime. The value of crime severities will be non-negative and will not exceed 109. OutputPrint a single integer — the number of ways you can choose the c prisoners.ExamplesInput4 3 32 3 1 1Output2Input1 1 12Output0Input11 4 22 2 0 7 3 2 2 4 9 1 4Output6	Input4 3 32 3 1 1	Output2	1 second	256 megabytes	['data structures', 'implementation', '*1100']
A. Police Recruitstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe police department of your city has just started its journey. Initially, they don’t have any manpower. So, they started hiring new recruits in groups.Meanwhile, crimes keeps occurring within the city. One member of the police force can investigate only one crime during his/her lifetime.If there is no police officer free (isn't busy with crime) during the occurrence of a crime, it will go untreated.Given the chronological order of crime occurrences and recruit hirings, find the number of crimes which will go untreated.InputThe first line of input will contain an integer n (1 ≤ n ≤ 105), the number of events. The next line will contain n space-separated integers.If the integer is -1 then it means a crime has occurred. Otherwise, the integer will be positive, the number of officers recruited together at that time. No more than 10 officers will be recruited at a time.OutputPrint a single integer, the number of crimes which will go untreated.ExamplesInput3-1 -1 1Output2Input81 -1 1 -1 -1 1 1 1Output1Input11-1 -1 2 -1 -1 -1 -1 -1 -1 -1 -1Output8NoteLets consider the second example: Firstly one person is hired. Then crime appears, the last hired person will investigate this crime. One more person is hired. One more crime appears, the last hired person will investigate this crime. Crime appears. There is no free policeman at the time, so this crime will go untreated. One more person is hired. One more person is hired. One more person is hired. The answer is one, as one crime (on step 5) will go untreated.	Input3-1 -1 1	Output2	1 second	256 megabytes	['implementation', '*800']
B. Sereja and Mirroringtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet's assume that we are given a matrix b of size x × y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x × y matrix c which has the following properties: the upper half of matrix c (rows with numbers from 1 to x) exactly matches b; the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1). Sereja has an n × m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?InputThe first line contains two integers, n and m (1 ≤ n, m ≤ 100). Each of the next n lines contains m integers — the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 ≤ aij ≤ 1) — the i-th row of the matrix a.OutputIn the single line, print the answer to the problem — the minimum number of rows of matrix b.ExamplesInput4 30 0 11 1 01 1 00 0 1Output2Input3 30 0 00 0 00 0 0Output3Input8 101100110Output2NoteIn the first test sample the answer is a 2 × 3 matrix b:001110If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:001110110001	Input4 30 0 11 1 01 1 00 0 1	Output2	1 second	256 megabytes	['implementation', '*1300']
A. Sereja and Mugstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputSereja showed an interesting game to his friends. The game goes like that. Initially, there is a table with an empty cup and n water mugs on it. Then all players take turns to move. During a move, a player takes a non-empty mug of water and pours all water from it into the cup. If the cup overfills, then we assume that this player lost.As soon as Sereja's friends heard of the game, they wanted to play it. Sereja, on the other hand, wanted to find out whether his friends can play the game in such a way that there are no losers. You are given the volumes of all mugs and the cup. Also, you know that Sereja has (n - 1) friends. Determine if Sereja's friends can play the game so that nobody loses.InputThe first line contains integers n and s (2 ≤ n ≤ 100; 1 ≤ s ≤ 1000) — the number of mugs and the volume of the cup. The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 10). Number ai means the volume of the i-th mug.OutputIn a single line, print "YES" (without the quotes) if his friends can play in the described manner, and "NO" (without the quotes) otherwise.ExamplesInput3 41 1 1OutputYESInput3 43 1 3OutputYESInput3 44 4 4OutputNO	Input3 41 1 1	OutputYES	1 second	256 megabytes	['implementation', '*800']
E. Sereja and Setstime limit per test1.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet's assume that set S consists of m distinct intervals [l1, r1], [l2, r2], ..., [lm, rm] (1 ≤ li ≤ ri ≤ n; li, ri are integers).Let's assume that f(S) is the maximum number of intervals that you can choose from the set S, such that every two of them do not intersect. We assume that two intervals, [l1, r1] and [l2, r2], intersect if there is an integer x, which meets two inequalities: l1 ≤ x ≤ r1 and l2 ≤ x ≤ r2.Sereja wonders, how many sets S are there, such that f(S) = k? Count this number modulo 1000000007 (109 + 7).InputThe first line contains integers n, k (1 ≤ n ≤ 500; 0 ≤ k ≤ 500).OutputIn a single line, print the answer to the problem modulo 1000000007 (109 + 7).ExamplesInput3 1Output23Input3 2Output32Input2 0Output1Input2 2Output2	Input3 1	Output23	1.5 seconds	256 megabytes	['dp', '*2500']
D. Sereja and Squarestime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputSereja has painted n distinct points on the plane. The coordinates of each point are integers. Now he is wondering: how many squares are there with sides parallel to the coordinate axes and with points painted in all its four vertexes? Help him, calculate this number.InputThe first line contains integer n (1 ≤ n ≤ 105). Each of the next n lines contains two integers xi, yi (0 ≤ xi, yi ≤ 105), the integers represent the coordinates of the i-th point. It is guaranteed that all the given points are distinct.OutputIn a single line print the required number of squares.ExamplesInput50 00 22 02 21 1Output1Input90 01 12 20 11 00 22 01 22 1Output5	Input50 00 22 02 21 1	Output1	2 seconds	512 megabytes	['binary search', 'data structures', 'hashing', '*2300']
C. Sereja and Two Sequencestime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputSereja has two sequences a1, a2, ..., an and b1, b2, ..., bm, consisting of integers. One day Sereja got bored and he decided two play with them. The rules of the game was very simple. Sereja makes several moves, in one move he can perform one of the following actions: Choose several (at least one) first elements of sequence a (non-empty prefix of a), choose several (at least one) first elements of sequence b (non-empty prefix of b); the element of sequence a with the maximum index among the chosen ones must be equal to the element of sequence b with the maximum index among the chosen ones; remove the chosen elements from the sequences. Remove all elements of both sequences. The first action is worth e energy units and adds one dollar to Sereja's electronic account. The second action is worth the number of energy units equal to the number of elements Sereja removed from the sequences before performing this action. After Sereja performed the second action, he gets all the money that he earned on his electronic account during the game.Initially Sereja has s energy units and no money on his account. What maximum number of money can Sereja get? Note, the amount of Seraja's energy mustn't be negative at any time moment.InputThe first line contains integers n, m, s, e (1 ≤ n, m ≤ 105; 1 ≤ s ≤ 3·105; 103 ≤ e ≤ 104). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105). The third line contains m integers b1, b2, ..., bm (1 ≤ bi ≤ 105).OutputPrint a single integer — maximum number of money in dollars that Sereja can get.ExamplesInput5 5 100000 10001 2 3 4 53 2 4 5 1Output3Input3 4 3006 10001 2 31 2 4 3Output2	Input5 5 100000 10001 2 3 4 53 2 4 5 1	Output3	4 seconds	512 megabytes	['data structures', 'dp', '*2300']
B. Sereja and Table time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputSereja has an n × m rectangular table a, each cell of the table contains a zero or a number one. Sereja wants his table to meet the following requirement: each connected component of the same values forms a rectangle with sides parallel to the sides of the table. Rectangles should be filled with cells, that is, if a component form a rectangle of size h × w, then the component must contain exactly hw cells.A connected component of the same values is a set of cells of the table that meet the following conditions: every two cells of the set have the same value; the cells of the set form a connected region on the table (two cells are connected if they are adjacent in some row or some column of the table); it is impossible to add any cell to the set unless we violate the two previous conditions. Can Sereja change the values of at most k cells of the table so that the table met the described requirement? What minimum number of table cells should he change in this case?InputThe first line contains integers n, m and k (1 ≤ n, m ≤ 100; 1 ≤ k ≤ 10). Next n lines describe the table a: the i-th of them contains m integers ai1, ai2, ..., aim (0 ≤ ai, j ≤ 1) — the values in the cells of the i-th row.OutputPrint -1, if it is impossible to meet the requirement. Otherwise, print the minimum number of cells which should be changed.ExamplesInput5 5 21 1 1 1 11 1 1 1 11 1 0 1 11 1 1 1 11 1 1 1 1Output1Input3 4 11 0 0 00 1 1 11 1 1 0Output-1Input3 4 11 0 0 10 1 1 01 0 0 1Output0	Input5 5 21 1 1 1 11 1 1 1 11 1 0 1 11 1 1 1 11 1 1 1 1	Output1	1 second	256 megabytes	['bitmasks', 'greedy', '*2200']
A. Sereja and Swapstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAs usual, Sereja has array a, its elements are integers: a[1], a[2], ..., a[n]. Let's introduce notation:A swap operation is the following sequence of actions: choose two indexes i, j (i ≠ j); perform assignments tmp = a[i], a[i] = a[j], a[j] = tmp. What maximum value of function m(a) can Sereja get if he is allowed to perform at most k swap operations?InputThe first line contains two integers n and k (1 ≤ n ≤ 200; 1 ≤ k ≤ 10). The next line contains n integers a[1], a[2], ..., a[n] ( - 1000 ≤ a[i] ≤ 1000).OutputIn a single line print the maximum value of m(a) that Sereja can get if he is allowed to perform at most k swap operations.ExamplesInput10 210 -1 2 2 2 2 2 2 -1 10Output32Input5 10-1 -1 -1 -1 -1Output-1	Input10 210 -1 2 2 2 2 2 2 -1 10	Output32	1 second	256 megabytes	['brute force', 'sortings', '*1500']
E. Colored Jengatime limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputCold winter evenings in Tomsk are very boring — nobody wants be on the streets at such a time. Residents of Tomsk while away the time sitting in warm apartments, inventing a lot of different games. One of such games is 'Colored Jenga'.This game requires wooden blocks of three colors: red, green and blue. A tower of n levels is made from them. Each level consists of three wooden blocks. The blocks in each level can be of arbitrary colors, but they are always located close and parallel to each other. An example of such a tower is shown in the figure. The game is played by exactly one person. Every minute a player throws a special dice which has six sides. Two sides of the dice are green, two are blue, one is red and one is black. The dice shows each side equiprobably.If the dice shows red, green or blue, the player must take any block of this color out of the tower at this minute so that the tower doesn't fall. If this is not possible, the player waits until the end of the minute, without touching the tower. He also has to wait until the end of the minute without touching the tower if the dice shows the black side. It is not allowed to take blocks from the top level of the tower (whether it is completed or not).Once a player got a block out, he must put it on the top of the tower so as to form a new level or finish the upper level consisting of previously placed blocks. The newly constructed levels should have all the same properties as the initial levels. If the upper level is not completed, starting the new level is prohibited.For the tower not to fall, in each of the levels except for the top, there should be at least one block. Moreover, if at some of these levels there is exactly one block left and this block is not the middle block, the tower falls.The game ends at the moment when there is no block in the tower that you can take out so that the tower doesn't fall.Here is a wonderful game invented by the residents of the city of Tomsk. I wonder for how many minutes can the game last if the player acts optimally well? If a player acts optimally well, then at any moment he tries to choose the block he takes out so as to minimize the expected number of the game duration.Your task is to write a program that determines the expected number of the desired amount of minutes.InputThe first line of the input contains the only integer n (2 ≤ n ≤ 6) — the number of levels in the tower.Then n lines follow, describing the levels of the tower from the bottom to the top (the first line is the top of the tower). Each level is described by three characters, the first and the third of them set the border blocks of the level and the second one is the middle block. The character that describes the block has one of the following values 'R' (a red block), 'G' (a green block) and 'B' (a blue block).OutputIn the only line of the output print the sought mathematical expectation value. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.ExamplesInput6RGBGRGBBBGGRBRGBRBOutput17.119213696601992	Input6RGBGRGBBBGGRBRGBRB	Output17.119213696601992	5 seconds	256 megabytes	['dfs and similar', 'dp', 'probabilities', '*2500']
D. Biathlon Tracktime limit per test4.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputRecently an official statement of the world Olympic Committee said that the Olympic Winter Games 2030 will be held in Tomsk. The city officials decided to prepare for the Olympics thoroughly and to build all the necessary Olympic facilities as early as possible. First, a biathlon track will be built.To construct a biathlon track a plot of land was allocated, which is a rectangle divided into n × m identical squares. Each of the squares has two coordinates: the number of the row (from 1 to n), where it is located, the number of the column (from 1 to m), where it is located. Also each of the squares is characterized by its height. During the sports the biathletes will have to move from one square to another. If a biathlete moves from a higher square to a lower one, he makes a descent. If a biathlete moves from a lower square to a higher one, he makes an ascent. If a biathlete moves between two squares with the same height, then he moves on flat ground.The biathlon track should be a border of some rectangular area of the allocated land on which biathletes will move in the clockwise direction. It is known that on one move on flat ground an average biathlete spends tp seconds, an ascent takes tu seconds, a descent takes td seconds. The Tomsk Administration wants to choose the route so that the average biathlete passes it in as close to t seconds as possible. In other words, the difference between time ts of passing the selected track and t should be minimum.For a better understanding you can look at the first sample of the input data. In this sample n = 6, m = 7, and the administration wants the track covering time to be as close to t = 48 seconds as possible, also, tp = 3, tu = 6 and td = 2. If we consider the rectangle shown on the image by arrows, the average biathlete can move along the boundary in a clockwise direction in exactly 48 seconds. The upper left corner of this track is located in the square with the row number 4, column number 3 and the lower right corner is at square with row number 6, column number 7. Among other things the administration wants all sides of the rectangle which boundaries will be the biathlon track to consist of no less than three squares and to be completely contained within the selected land.You are given the description of the given plot of land and all necessary time values. You are to write the program to find the most suitable rectangle for a biathlon track. If there are several such rectangles, you are allowed to print any of them.InputThe first line of the input contains three integers n, m and t (3 ≤ n, m ≤ 300, 1 ≤ t ≤ 109) — the sizes of the land plot and the desired distance covering time.The second line also contains three integers tp, tu and td (1 ≤ tp, tu, td ≤ 100) — the time the average biathlete needs to cover a flat piece of the track, an ascent and a descent respectively.Then n lines follow, each line contains m integers that set the heights of each square of the given plot of land. Each of the height values is a positive integer, not exceeding 106.OutputIn a single line of the output print four positive integers — the number of the row and the number of the column of the upper left corner and the number of the row and the number of the column of the lower right corner of the rectangle that is chosen for the track.ExamplesInput6 7 483 6 25 4 8 3 3 7 94 1 6 8 7 1 11 6 4 6 4 8 67 2 6 1 6 9 41 9 8 6 3 9 24 5 6 8 4 3 7Output4 3 6 7	Input6 7 483 6 25 4 8 3 3 7 94 1 6 8 7 1 11 6 4 6 4 8 67 2 6 1 6 9 41 9 8 6 3 9 24 5 6 8 4 3 7	Output4 3 6 7	4.5 seconds	256 megabytes	['binary search', 'brute force', 'constructive algorithms', 'data structures', 'dp', '*2300']
C. Magic Formulastime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputPeople in the Tomskaya region like magic formulas very much. You can see some of them below.Imagine you are given a sequence of positive integer numbers p1, p2, ..., pn. Lets write down some magic formulas:Here, "mod" means the operation of taking the residue after dividing.The expression means applying the bitwise xor (excluding "OR") operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by "^", in Pascal — by "xor".People in the Tomskaya region like magic formulas very much, but they don't like to calculate them! Therefore you are given the sequence p, calculate the value of Q.InputThe first line of the input contains the only integer n (1 ≤ n ≤ 106). The next line contains n integers: p1, p2, ..., pn (0 ≤ pi ≤ 2·109).OutputThe only line of output should contain a single integer — the value of Q.ExamplesInput31 2 3Output3	Input31 2 3	Output3	2 seconds	256 megabytes	['math', '*1600']
B. Megacitytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe administration of the Tomsk Region firmly believes that it's time to become a megacity (that is, get population of one million). Instead of improving the demographic situation, they decided to achieve its goal by expanding the boundaries of the city.The city of Tomsk can be represented as point on the plane with coordinates (0; 0). The city is surrounded with n other locations, the i-th one has coordinates (xi, yi) with the population of ki people. You can widen the city boundaries to a circle of radius r. In such case all locations inside the circle and on its border are included into the city.Your goal is to write a program that will determine the minimum radius r, to which is necessary to expand the boundaries of Tomsk, so that it becomes a megacity.InputThe first line of the input contains two integers n and s (1 ≤ n ≤ 103; 1 ≤ s < 106) — the number of locatons around Tomsk city and the population of the city. Then n lines follow. The i-th line contains three integers — the xi and yi coordinate values of the i-th location and the number ki of people in it (1 ≤ ki < 106). Each coordinate is an integer and doesn't exceed 104 in its absolute value.It is guaranteed that no two locations are at the same point and no location is at point (0; 0).OutputIn the output, print "-1" (without the quotes), if Tomsk won't be able to become a megacity. Otherwise, in the first line print a single real number — the minimum radius of the circle that the city needs to expand to in order to become a megacity.The answer is considered correct if the absolute or relative error don't exceed 10 - 6.ExamplesInput4 9999981 1 12 2 13 3 12 -2 1Output2.8284271Input4 9999981 1 22 2 13 3 12 -2 1Output1.4142136Input2 11 1 9999972 2 1Output-1	Input4 9999981 1 12 2 13 3 12 -2 1	Output2.8284271	2 seconds	256 megabytes	['binary search', 'greedy', 'implementation', 'sortings', '*1200']
A. Squatstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputPasha has many hamsters and he makes them work out. Today, n hamsters (n is even) came to work out. The hamsters lined up and each hamster either sat down or stood up.For another exercise, Pasha needs exactly hamsters to stand up and the other hamsters to sit down. In one minute, Pasha can make some hamster ether sit down or stand up. How many minutes will he need to get what he wants if he acts optimally well?InputThe first line contains integer n (2 ≤ n ≤ 200; n is even). The next line contains n characters without spaces. These characters describe the hamsters' position: the i-th character equals 'X', if the i-th hamster in the row is standing, and 'x', if he is sitting.OutputIn the first line, print a single integer — the minimum required number of minutes. In the second line, print a string that describes the hamsters' position after Pasha makes the required changes. If there are multiple optimal positions, print any of them.ExamplesInput4xxXxOutput1XxXxInput2XXOutput1xXInput6xXXxXxOutput0xXXxXx	Input4xxXx	Output1XxXx	1 second	256 megabytes	['implementation', '*900']
D. Bug in Codetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputRecently a serious bug has been found in the FOS code. The head of the F company wants to find the culprit and punish him. For that, he set up an organizational meeting, the issue is: who's bugged the code? Each of the n coders on the meeting said: 'I know for sure that either x or y did it!'The head of the company decided to choose two suspects and invite them to his office. Naturally, he should consider the coders' opinions. That's why the head wants to make such a choice that at least p of n coders agreed with it. A coder agrees with the choice of two suspects if at least one of the two people that he named at the meeting was chosen as a suspect. In how many ways can the head of F choose two suspects?Note that even if some coder was chosen as a suspect, he can agree with the head's choice if he named the other chosen coder at the meeting.InputThe first line contains integers n and p (3 ≤ n ≤ 3·105; 0 ≤ p ≤ n) — the number of coders in the F company and the minimum number of agreed people.Each of the next n lines contains two integers xi, yi (1 ≤ xi, yi ≤ n) — the numbers of coders named by the i-th coder. It is guaranteed that xi ≠ i, yi ≠ i, xi ≠ yi.OutputPrint a single integer — the number of possible two-suspect sets. Note that the order of the suspects doesn't matter, that is, sets (1, 2) and (2, 1) are considered identical.ExamplesInput4 22 31 41 42 1Output6Input8 65 65 75 86 22 17 31 31 4Output1	Input4 22 31 41 42 1	Output6	1 second	256 megabytes	['binary search', 'data structures', 'sortings', '*1900']
A. Pasha and Hamsterstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputPasha has two hamsters: Arthur and Alexander. Pasha put n apples in front of them. Pasha knows which apples Arthur likes. Similarly, Pasha knows which apples Alexander likes. Pasha doesn't want any conflict between the hamsters (as they may like the same apple), so he decided to distribute the apples between the hamsters on his own. He is going to give some apples to Arthur and some apples to Alexander. It doesn't matter how many apples each hamster gets but it is important that each hamster gets only the apples he likes. It is possible that somebody doesn't get any apples.Help Pasha distribute all the apples between the hamsters. Note that Pasha wants to distribute all the apples, not just some of them.InputThe first line contains integers n, a, b (1 ≤ n ≤ 100; 1 ≤ a, b ≤ n) — the number of apples Pasha has, the number of apples Arthur likes and the number of apples Alexander likes, correspondingly.The next line contains a distinct integers — the numbers of the apples Arthur likes. The next line contains b distinct integers — the numbers of the apples Alexander likes.Assume that the apples are numbered from 1 to n. The input is such that the answer exists.OutputPrint n characters, each of them equals either 1 or 2. If the i-h character equals 1, then the i-th apple should be given to Arthur, otherwise it should be given to Alexander. If there are multiple correct answers, you are allowed to print any of them.ExamplesInput4 2 31 22 3 4Output1 1 2 2Input5 5 23 4 1 2 52 3Output1 1 1 1 1	Input4 2 31 22 3 4	Output1 1 2 2	1 second	256 megabytes	['constructive algorithms', 'implementation', '*800']
E. Playing the balltime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA coder cannot sit and code all day. Sometimes it is a good idea to rise from the desk, have a rest, have small talk with colleagues and even play. The coders of the F company have their favorite ball game.Let's imagine the game on the plane with a cartesian coordinate system. The point (0, 0) contains the player who chooses an arbitrary direction and throws a ball in that direction. The ball hits the plane at distance d from the player's original position and continues flying in the same direction. After the ball hits the plane for the first time, it flies on and hits the plane again at distance 2·d from the player's original position and so on (it continue flying in the chosen direction and hitting the plane after each d units). All coders in the F company are strong, so the ball flies infinitely far away.The plane has n circles painted on it. If a ball hits the plane and hits a circle that is painted on the plane (including its border), then the player gets one point. The ball can hit multiple circles at once and get one point for each of them (if the ball hits some circle x times during the move, the player also gets x points). Count the maximum number of points a player can get if he throws a ball in the arbitrary direction. Note that the direction may have real cooridinates.InputThe first line contains two space-separated integers — n и d (1 ≤ n ≤ 2·104; 5 ≤ d ≤ 10). Next n lines contain the circles' description. The i-th line contains three space-separated integers xi, yi, ri ( - 10000 ≤ xi, yi ≤ 10000; 1 ≤ r ≤ 50), where (xi, yi, ri) are the coordinates of the center and the radius of the circle, correspondingly. The point (0, 0) is not inside or on the border of some circle.OutputPrint a single integer — the maximum number of points you can get.ExamplesInput2 51 1 15 0 1Output1Input2 54 0 35 3 1Output2Input1 1020 0 10Output3	Input2 51 1 15 0 1	Output1	2 seconds	256 megabytes	['geometry', '*2600']
D. Cup Tricktime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe employees of the F company have lots of ways to entertain themselves. Today they invited a famous magician who shows a trick with plastic cups and a marble.The point is to trick the spectator's attention. Initially, the spectator stands in front of a line of n plastic cups. Then the magician places a small marble under one cup and shuffles the cups. Then the spectator should guess which cup hides the marble.But the head coder of the F company isn't easy to trick. When he saw the performance, he noticed several important facts: each cup contains a mark — a number from 1 to n; all marks on the cups are distinct; the magician shuffles the cups in m operations, each operation looks like that: take a cup marked xi, sitting at position yi in the row of cups (the positions are numbered from left to right, starting from 1) and shift it to the very beginning of the cup row (on the first position). When the head coder came home after work he wanted to re-do the trick. Unfortunately, he didn't remember the starting or the final position of the cups. He only remembered which operations the magician performed. Help the coder: given the operations in the order they were made find at least one initial permutation of the cups that can go through the described operations in the given order. Otherwise, state that such permutation doesn't exist.InputThe first line contains integers n and m (1 ≤ n, m ≤ 106). Each of the next m lines contains a couple of integers. The i-th line contains integers xi, yi (1 ≤ xi, yi ≤ n) — the description of the i-th operation of the magician. Note that the operations are given in the order in which the magician made them and the coder wants to make them in the same order.OutputIf the described permutation doesn't exist (the programmer remembered wrong operations), print -1. Otherwise, print n distinct integers, each from 1 to n: the i-th number should represent the mark on the cup that initially is in the row in position i.If there are multiple correct answers, you should print the lexicographically minimum one.ExamplesInput2 12 1Output2 1 Input3 21 21 1Output2 1 3 Input3 31 32 31 3Output-1	Input2 12 1	Output2 1	3 seconds	256 megabytes	['data structures', '*2200']
C. Bug in Codetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputRecently a serious bug has been found in the FOS code. The head of the F company wants to find the culprit and punish him. For that, he set up an organizational meeting, the issue is: who's bugged the code? Each of the n coders on the meeting said: 'I know for sure that either x or y did it!'The head of the company decided to choose two suspects and invite them to his office. Naturally, he should consider the coders' opinions. That's why the head wants to make such a choice that at least p of n coders agreed with it. A coder agrees with the choice of two suspects if at least one of the two people that he named at the meeting was chosen as a suspect. In how many ways can the head of F choose two suspects?Note that even if some coder was chosen as a suspect, he can agree with the head's choice if he named the other chosen coder at the meeting.InputThe first line contains integers n and p (3 ≤ n ≤ 3·105; 0 ≤ p ≤ n) — the number of coders in the F company and the minimum number of agreed people.Each of the next n lines contains two integers xi, yi (1 ≤ xi, yi ≤ n) — the numbers of coders named by the i-th coder. It is guaranteed that xi ≠ i, yi ≠ i, xi ≠ yi.OutputPrint a single integer –– the number of possible two-suspect sets. Note that the order of the suspects doesn't matter, that is, sets (1, 2) и (2, 1) are considered identical.ExamplesInput4 22 31 41 42 1Output6Input8 65 65 75 86 22 17 31 31 4Output1	Input4 22 31 41 42 1	Output6	1 second	256 megabytes	['data structures', 'graphs', 'implementation', 'two pointers', '*1900']
B. Online Meetingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputNearly each project of the F company has a whole team of developers working on it. They often are in different rooms of the office in different cities and even countries. To keep in touch and track the results of the project, the F company conducts shared online meetings in a Spyke chat.One day the director of the F company got hold of the records of a part of an online meeting of one successful team. The director watched the record and wanted to talk to the team leader. But how can he tell who the leader is? The director logically supposed that the leader is the person who is present at any conversation during a chat meeting. In other words, if at some moment of time at least one person is present on the meeting, then the leader is present on the meeting.You are the assistant director. Given the 'user logged on'/'user logged off' messages of the meeting in the chronological order, help the director determine who can be the leader. Note that the director has the record of only a continuous part of the meeting (probably, it's not the whole meeting).InputThe first line contains integers n and m (1 ≤ n, m ≤ 105) — the number of team participants and the number of messages. Each of the next m lines contains a message in the format: '+ id': the record means that the person with number id (1 ≤ id ≤ n) has logged on to the meeting. '- id': the record means that the person with number id (1 ≤ id ≤ n) has logged off from the meeting. Assume that all the people of the team are numbered from 1 to n and the messages are given in the chronological order. It is guaranteed that the given sequence is the correct record of a continuous part of the meeting. It is guaranteed that no two log on/log off events occurred simultaneously.OutputIn the first line print integer k (0 ≤ k ≤ n) — how many people can be leaders. In the next line, print k integers in the increasing order — the numbers of the people who can be leaders.If the data is such that no member of the team can be a leader, print a single number 0.ExamplesInput5 4+ 1+ 2- 2- 1Output41 3 4 5 Input3 2+ 1- 2Output13 Input2 4+ 1- 1+ 2- 2Output0Input5 6+ 1- 1- 3+ 3+ 4- 4Output32 3 5 Input2 4+ 1- 2+ 2- 1Output0	Input5 4+ 1+ 2- 2- 1	Output41 3 4 5	1 second	256 megabytes	['implementation', '*1800']
A. Start Uptime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputRecently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.InputThe first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font: OutputPrint 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).ExamplesInputAHAOutputYESInputZOutputNOInputXOOutputNO	InputAHA	OutputYES	1 second	256 megabytes	['implementation', '*1000']
E. Tricky Passwordtime limit per test3.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputIn order to ensure confidentiality, the access to the "Russian Code Cup" problems is password protected during the problem development process.To select a password, the jury can generate a special table that contains n columns and the infinite number of rows. To construct a table, the first row is fixed, and all the others are obtained by the following rule:In the row i at position p there is a number equal to the number of times a[i - 1][p] occurs on the prefix a[i - 1][1... p].To ensure the required level of confidentiality, the jury must be able to perform the following operations: Replace number a[1][p] by v and rebuild the table. Find the number a[x][y], which will be the new password. Doing all these steps manually is very tedious, so the jury asks you to help him. Write a program that responds to the request of the jury.InputThe first line contains an integer n (1 ≤ n ≤ 100000) — the number of columns. The second line contains the description of the first row of the table, that is, n integers, which are not less than 1 and do not exceed 109.The third line of the input contains an integer m (1 ≤ m ≤ 100000) — the number of requests.Next, each row contains a description of the request, which consists of three integers: If the first number is equal to 1, then the remaining two numbers are v, p (1 ≤ v ≤ 109; 1 ≤ p ≤ n). So, you should put value v in the position p in the first row. If the first number is equal to 2, then the remaining two numbers are x, y (1 ≤ x ≤ 105; 1 ≤ y ≤ n) — the row and column of the table cell from which you want to get value. OutputPrint an answer for each request of the second type in the order you receive them.ExamplesInput61 2 2 2 3 132 2 31 3 32 3 4Output21	Input61 2 2 2 3 132 2 31 3 32 3 4	Output21	3.5 seconds	512 megabytes	['data structures', '*3100']
D. Big Problems for Organizerstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe Finals of the "Russian Code Cup" 2214 will be held in n hotels. Two hotels (let's assume that they are the main hotels), will host all sorts of events, and the remaining hotels will accommodate the participants. The hotels are connected by n - 1 roads, you can get from any hotel to any other one.The organizers wonder what is the minimum time all the participants need to get to the main hotels, if each participant goes to the main hotel that is nearest to him and moving between two hotels connected by a road takes one unit of time.The hosts consider various options for the location of the main hotels. For each option help the organizers to find minimal time.InputThe first line contains an integer n (2 ≤ n ≤ 100000) — the number of hotels. The next n - 1 lines contain two integers each — the numbers of the hotels that have a road between them. Consider hotels are numbered from 1 to n.The next line contains an integer m (1 ≤ m ≤ 100000) — the number of queries. The following m lines contains two distinct integers each — the numbers of the hotels we assume to be the main.OutputFor each request of the organizers print a single integer — the time that all participants need to reach the main hotels.ExamplesInput32 33 132 12 33 1Output111Input41 41 22 331 41 32 3Output212	Input32 33 132 12 33 1	Output111	2 seconds	256 megabytes	['data structures', 'graphs', 'trees', '*2800']
E. Square Tabletime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputWhile resting on the ship after the "Russian Code Cup" a boy named Misha invented an interesting game. He promised to give his quadrocopter to whoever will be the first one to make a rectangular table of size n × m, consisting of positive integers such that the sum of the squares of numbers for each row and each column was also a square.Since checking the correctness of the table manually is difficult, Misha asks you to make each number in the table to not exceed 108.InputThe first line contains two integers n and m (1 ≤ n, m ≤ 100) — the size of the table. OutputPrint the table that meets the condition: n lines containing m integers, separated by spaces. If there are multiple possible answers, you are allowed to print anyone. It is guaranteed that there exists at least one correct answer.ExamplesInput1 1Output1Input1 2Output3 4	Input1 1	Output1	1 second	256 megabytes	['constructive algorithms', 'math', 'probabilities', '*2400']
D. Cunning Genatime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA boy named Gena really wants to get to the "Russian Code Cup" finals, or at least get a t-shirt. But the offered problems are too complex, so he made an arrangement with his n friends that they will solve the problems for him.The participants are offered m problems on the contest. For each friend, Gena knows what problems he can solve. But Gena's friends won't agree to help Gena for nothing: the i-th friend asks Gena xi rubles for his help in solving all the problems he can. Also, the friend agreed to write a code for Gena only if Gena's computer is connected to at least ki monitors, each monitor costs b rubles.Gena is careful with money, so he wants to spend as little money as possible to solve all the problems. Help Gena, tell him how to spend the smallest possible amount of money. Initially, there's no monitors connected to Gena's computer.InputThe first line contains three integers n, m and b (1 ≤ n ≤ 100; 1 ≤ m ≤ 20; 1 ≤ b ≤ 109) — the number of Gena's friends, the number of problems and the cost of a single monitor.The following 2n lines describe the friends. Lines number 2i and (2i + 1) contain the information about the i-th friend. The 2i-th line contains three integers xi, ki and mi (1 ≤ xi ≤ 109; 1 ≤ ki ≤ 109; 1 ≤ mi ≤ m) — the desired amount of money, monitors and the number of problems the friend can solve. The (2i + 1)-th line contains mi distinct positive integers — the numbers of problems that the i-th friend can solve. The problems are numbered from 1 to m.OutputPrint the minimum amount of money Gena needs to spend to solve all the problems. Or print -1, if this cannot be achieved.ExamplesInput2 2 1100 1 12100 2 11Output202Input3 2 5100 1 11100 1 12200 1 21 2Output205Input1 2 11 1 11Output-1	Input2 2 1100 1 12100 2 11	Output202	1 second	256 megabytes	['bitmasks', 'dp', 'greedy', 'sortings', '*1900']
C. Footballtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputOne day, at the "Russian Code Cup" event it was decided to play football as an out of competition event. All participants was divided into n teams and played several matches, two teams could not play against each other more than once.The appointed Judge was the most experienced member — Pavel. But since he was the wisest of all, he soon got bored of the game and fell asleep. Waking up, he discovered that the tournament is over and the teams want to know the results of all the matches.Pavel didn't want anyone to discover about him sleeping and not keeping an eye on the results, so he decided to recover the results of all games. To do this, he asked all the teams and learned that the real winner was friendship, that is, each team beat the other teams exactly k times. Help Pavel come up with chronology of the tournir that meets all the conditions, or otherwise report that there is no such table.InputThe first line contains two integers — n and k (1 ≤ n, k ≤ 1000).OutputIn the first line print an integer m — number of the played games. The following m lines should contain the information about all the matches, one match per line. The i-th line should contain two integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi). The numbers ai and bi mean, that in the i-th match the team with number ai won against the team with number bi. You can assume, that the teams are numbered from 1 to n.If a tournir that meets the conditions of the problem does not exist, then print -1.ExamplesInput3 1Output31 22 33 1	Input3 1	Output31 22 33 1	1 second	256 megabytes	['constructive algorithms', 'graphs', 'implementation', '*1400']
B. Crashtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputDuring the "Russian Code Cup" programming competition, the testing system stores all sent solutions for each participant. We know that many participants use random numbers in their programs and are often sent several solutions with the same source code to check.Each participant is identified by some unique positive integer k, and each sent solution A is characterized by two numbers: x — the number of different solutions that are sent before the first solution identical to A, and k — the number of the participant, who is the author of the solution. Consequently, all identical solutions have the same x.It is known that the data in the testing system are stored in the chronological order, that is, if the testing system has a solution with number x (x > 0) of the participant with number k, then the testing system has a solution with number x - 1 of the same participant stored somewhere before.During the competition the checking system crashed, but then the data of the submissions of all participants have been restored. Now the jury wants to verify that the recovered data is in chronological order. Help the jury to do so.InputThe first line of the input contains an integer n (1 ≤ n ≤ 105) — the number of solutions. Each of the following n lines contains two integers separated by space x and k (0 ≤ x ≤ 105; 1 ≤ k ≤ 105) — the number of previous unique solutions and the identifier of the participant.OutputA single line of the output should contain «YES» if the data is in chronological order, and «NO» otherwise.ExamplesInput20 11 1OutputYESInput40 11 21 10 2OutputNOInput40 11 10 10 2OutputYES	Input20 11 1	OutputYES	1 second	256 megabytes	['implementation', '*1400']
A. Eliminationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe finalists of the "Russian Code Cup" competition in 2214 will be the participants who win in one of the elimination rounds.The elimination rounds are divided into main and additional. Each of the main elimination rounds consists of c problems, the winners of the round are the first n people in the rating list. Each of the additional elimination rounds consists of d problems. The winner of the additional round is one person. Besides, k winners of the past finals are invited to the finals without elimination.As a result of all elimination rounds at least n·m people should go to the finals. You need to organize elimination rounds in such a way, that at least n·m people go to the finals, and the total amount of used problems in all rounds is as small as possible.InputThe first line contains two integers c and d (1 ≤ c, d ≤ 100) — the number of problems in the main and additional rounds, correspondingly. The second line contains two integers n and m (1 ≤ n, m ≤ 100). Finally, the third line contains an integer k (1 ≤ k ≤ 100) — the number of the pre-chosen winners. OutputIn the first line, print a single integer — the minimum number of problems the jury needs to prepare.ExamplesInput1 107 21Output2Input2 22 12Output0	Input1 107 21	Output2	1 second	256 megabytes	['dp', 'implementation', 'math', '*1500']
E. President's Pathtime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputGood old Berland has n cities and m roads. Each road connects a pair of distinct cities and is bidirectional. Between any pair of cities, there is at most one road. For each road, we know its length.We also know that the President will soon ride along the Berland roads from city s to city t. Naturally, he will choose one of the shortest paths from s to t, but nobody can say for sure which path he will choose.The Minister for Transport is really afraid that the President might get upset by the state of the roads in the country. That is the reason he is planning to repair the roads in the possible President's path.Making the budget for such an event is not an easy task. For all possible distinct pairs s, t (s < t) find the number of roads that lie on at least one shortest path from s to t.InputThe first line of the input contains integers n, m (2 ≤ n ≤ 500, 0 ≤ m ≤ n·(n - 1) / 2) — the number of cities and roads, correspondingly. Then m lines follow, containing the road descriptions, one description per line. Each description contains three integers xi, yi, li (1 ≤ xi, yi ≤ n, xi ≠ yi, 1 ≤ li ≤ 106), where xi, yi are the numbers of the cities connected by the i-th road and li is its length.OutputPrint the sequence of integers c12, c13, ..., c1n, c23, c24, ..., c2n, ..., cn - 1, n, where cst is the number of roads that can lie on the shortest path from s to t. Print the elements of sequence c in the described order. If the pair of cities s and t don't have a path between them, then cst = 0.ExamplesInput5 61 2 12 3 13 4 14 1 12 4 24 5 4Output1 4 1 2 1 5 6 1 2 1	Input5 61 2 12 3 13 4 14 1 12 4 24 5 4	Output1 4 1 2 1 5 6 1 2 1	4 seconds	256 megabytes	['dp', 'graphs', 'shortest paths', '*2500']
D. Population Sizetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputPolycarpus develops an interesting theory about the interrelation of arithmetic progressions with just everything in the world. His current idea is that the population of the capital of Berland changes over time like an arithmetic progression. Well, or like multiple arithmetic progressions.Polycarpus believes that if he writes out the population of the capital for several consecutive years in the sequence a1, a2, ..., an, then it is convenient to consider the array as several arithmetic progressions, written one after the other. For example, sequence (8, 6, 4, 2, 1, 4, 7, 10, 2) can be considered as a sequence of three arithmetic progressions (8, 6, 4, 2), (1, 4, 7, 10) and (2), which are written one after another.Unfortunately, Polycarpus may not have all the data for the n consecutive years (a census of the population doesn't occur every year, after all). For this reason, some values of ai may be unknown. Such values are represented by number -1.For a given sequence a = (a1, a2, ..., an), which consists of positive integers and values -1, find the minimum number of arithmetic progressions Polycarpus needs to get a. To get a, the progressions need to be written down one after the other. Values -1 may correspond to an arbitrary positive integer and the values ai > 0 must be equal to the corresponding elements of sought consecutive record of the progressions.Let us remind you that a finite sequence c is called an arithmetic progression if the difference ci + 1 - ci of any two consecutive elements in it is constant. By definition, any sequence of length 1 is an arithmetic progression.InputThe first line of the input contains integer n (1 ≤ n ≤ 2·105) — the number of elements in the sequence. The second line contains integer values a1, a2, ..., an separated by a space (1 ≤ ai ≤ 109 or ai = - 1).OutputPrint the minimum number of arithmetic progressions that you need to write one after another to get sequence a. The positions marked as -1 in a can be represented by any positive integers.ExamplesInput98 6 4 2 1 4 7 10 2Output3Input9-1 6 -1 2 -1 4 7 -1 2Output3Input5-1 -1 -1 -1 -1Output1Input7-1 -1 4 5 1 2 3Output2	Input98 6 4 2 1 4 7 10 2	Output3	1 second	256 megabytes	['greedy', 'implementation', 'math', '*2400']
C. Booking Systemtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputInnovation technologies are on a victorious march around the planet. They integrate into all spheres of human activity!A restaurant called "Dijkstra's Place" has started thinking about optimizing the booking system. There are n booking requests received by now. Each request is characterized by two numbers: ci and pi — the size of the group of visitors who will come via this request and the total sum of money they will spend in the restaurant, correspondingly.We know that for each request, all ci people want to sit at the same table and are going to spend the whole evening in the restaurant, from the opening moment at 18:00 to the closing moment.Unfortunately, there only are k tables in the restaurant. For each table, we know ri — the maximum number of people who can sit at it. A table can have only people from the same group sitting at it. If you cannot find a large enough table for the whole group, then all visitors leave and naturally, pay nothing.Your task is: given the tables and the requests, decide which requests to accept and which requests to decline so that the money paid by the happy and full visitors was maximum.InputThe first line of the input contains integer n (1 ≤ n ≤ 1000) — the number of requests from visitors. Then n lines follow. Each line contains two integers: ci, pi (1 ≤ ci, pi ≤ 1000) — the size of the group of visitors who will come by the i-th request and the total sum of money they will pay when they visit the restaurant, correspondingly.The next line contains integer k (1 ≤ k ≤ 1000) — the number of tables in the restaurant. The last line contains k space-separated integers: r1, r2, ..., rk (1 ≤ ri ≤ 1000) — the maximum number of people that can sit at each table.OutputIn the first line print two integers: m, s — the number of accepted requests and the total money you get from these requests, correspondingly.Then print m lines — each line must contain two space-separated integers: the number of the accepted request and the number of the table to seat people who come via this request. The requests and the tables are consecutively numbered starting from 1 in the order in which they are given in the input.If there are multiple optimal answers, print any of them.ExamplesInput310 502 1005 3034 6 9Output2 1302 13 2	Input310 502 1005 3034 6 9	Output2 1302 13 2	1 second	256 megabytes	['binary search', 'dp', 'greedy', 'implementation', '*1600']
B. Art Uniontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA well-known art union called "Kalevich is Alive!" manufactures objects d'art (pictures). The union consists of n painters who decided to organize their work as follows.Each painter uses only the color that was assigned to him. The colors are distinct for all painters. Let's assume that the first painter uses color 1, the second one uses color 2, and so on. Each picture will contain all these n colors. Adding the j-th color to the i-th picture takes the j-th painter tij units of time.Order is important everywhere, so the painters' work is ordered by the following rules: Each picture is first painted by the first painter, then by the second one, and so on. That is, after the j-th painter finishes working on the picture, it must go to the (j + 1)-th painter (if j < n); each painter works on the pictures in some order: first, he paints the first picture, then he paints the second picture and so on; each painter can simultaneously work on at most one picture. However, the painters don't need any time to have a rest; as soon as the j-th painter finishes his part of working on the picture, the picture immediately becomes available to the next painter. Given that the painters start working at time 0, find for each picture the time when it is ready for sale.InputThe first line of the input contains integers m, n (1 ≤ m ≤ 50000, 1 ≤ n ≤ 5), where m is the number of pictures and n is the number of painters. Then follow the descriptions of the pictures, one per line. Each line contains n integers ti1, ti2, ..., tin (1 ≤ tij ≤ 1000), where tij is the time the j-th painter needs to work on the i-th picture.OutputPrint the sequence of m integers r1, r2, ..., rm, where ri is the moment when the n-th painter stopped working on the i-th picture.ExamplesInput5 112345Output1 3 6 10 15 Input4 22 53 15 310 1Output7 8 13 21	Input5 112345	Output1 3 6 10 15	1 second	256 megabytes	['brute force', 'dp', 'implementation', '*1300']
A. Guess a number!time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA TV show called "Guess a number!" is gathering popularity. The whole Berland, the old and the young, are watching the show.The rules are simple. The host thinks of an integer y and the participants guess it by asking questions to the host. There are four types of acceptable questions: Is it true that y is strictly larger than number x? Is it true that y is strictly smaller than number x? Is it true that y is larger than or equal to number x? Is it true that y is smaller than or equal to number x? On each question the host answers truthfully, "yes" or "no".Given the sequence of questions and answers, find any integer value of y that meets the criteria of all answers. If there isn't such value, print "Impossible".InputThe first line of the input contains a single integer n (1 ≤ n ≤ 10000) — the number of questions (and answers). Next n lines each contain one question and one answer to it. The format of each line is like that: "sign x answer", where the sign is: ">" (for the first type queries), "<" (for the second type queries), ">=" (for the third type queries), "<=" (for the fourth type queries). All values of x are integer and meet the inequation - 109 ≤ x ≤ 109. The answer is an English letter "Y" (for "yes") or "N" (for "no").Consequtive elements in lines are separated by a single space.OutputPrint any of such integers y, that the answers to all the queries are correct. The printed number y must meet the inequation - 2·109 ≤ y ≤ 2·109. If there are many answers, print any of them. If such value doesn't exist, print word "Impossible" (without the quotes).ExamplesInput4>= 1 Y< 3 N<= -3 N> 55 NOutput17Input2> 100 Y< -100 YOutputImpossible	Input4>= 1 Y< 3 N<= -3 N> 55 N	Output17	1 second	256 megabytes	['greedy', 'implementation', 'two pointers', '*1400']
B. Mashmokh and Tokenstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputBimokh is Mashmokh's boss. For the following n days he decided to pay to his workers in a new way. At the beginning of each day he will give each worker a certain amount of tokens. Then at the end of each day each worker can give some of his tokens back to get a certain amount of money. The worker can save the rest of tokens but he can't use it in any other day to get more money. If a worker gives back w tokens then he'll get dollars. Mashmokh likes the tokens however he likes money more. That's why he wants to save as many tokens as possible so that the amount of money he gets is maximal possible each day. He has n numbers x1, x2, ..., xn. Number xi is the number of tokens given to each worker on the i-th day. Help him calculate for each of n days the number of tokens he can save.InputThe first line of input contains three space-separated integers n, a, b (1 ≤ n ≤ 105; 1 ≤ a, b ≤ 109). The second line of input contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 109).OutputOutput n space-separated integers. The i-th of them is the number of tokens Mashmokh can save on the i-th day.ExamplesInput5 1 412 6 11 9 1Output0 2 3 1 1 Input3 1 21 2 3Output1 0 1 Input1 1 11Output0	Input5 1 412 6 11 9 1	Output0 2 3 1 1	1 second	256 megabytes	['binary search', 'greedy', 'implementation', 'math', '*1500']
A. Mashmokh and Lightstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputMashmokh works in a factory. At the end of each day he must turn off all of the lights. The lights on the factory are indexed from 1 to n. There are n buttons in Mashmokh's room indexed from 1 to n as well. If Mashmokh pushes button with index i, then each light with index not less than i that is still turned on turns off.Mashmokh is not very clever. So instead of pushing the first button he pushes some of the buttons randomly each night. He pushed m distinct buttons b1, b2, ..., bm (the buttons were pushed consecutively in the given order) this night. Now he wants to know for each light the index of the button that turned this light off. Please note that the index of button bi is actually bi, not i.Please, help Mashmokh, print these indices.InputThe first line of the input contains two space-separated integers n and m (1 ≤ n, m ≤ 100), the number of the factory lights and the pushed buttons respectively. The next line contains m distinct space-separated integers b1, b2, ..., bm (1 ≤ bi ≤ n).It is guaranteed that all lights will be turned off after pushing all buttons.OutputOutput n space-separated integers where the i-th number is index of the button that turns the i-th light off.ExamplesInput5 44 3 1 2Output1 1 3 4 4 Input5 55 4 3 2 1Output1 2 3 4 5 NoteIn the first sample, after pressing button number 4, lights 4 and 5 are turned off and lights 1, 2 and 3 are still on. Then after pressing button number 3, light number 3 is turned off as well. Pressing button number 1 turns off lights number 1 and 2 as well so pressing button number 2 in the end has no effect. Thus button number 4 turned lights 4 and 5 off, button number 3 turned light 3 off and button number 1 turned light 1 and 2 off.	Input5 44 3 1 2	Output1 1 3 4 4	1 second	256 megabytes	['implementation', '*900']
E. Mashmokh's Designed Problemtime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputAfter a lot of trying, Mashmokh designed a problem and it's your job to solve it.You have a tree T with n vertices. Each vertex has a unique index from 1 to n. The root of T has index 1. For each vertex of this tree v, you are given a list of its children in a specific order. You must perform three types of query on this tree: find distance (the number of edges in the shortest path) between u and v; given v and h, disconnect v from its father and connect it to its h-th ancestor; more formally, let's denote the path from v to the root by x1, x2, ..., xl (h < l), so that x1 = v and xl is root; disconnect v from its father (x2) and connect it to xh + 1; vertex v must be added to the end of the child-list of vertex xh + 1; in the vertex sequence produced by calling function dfs(root) find the latest vertex that has distance k from the root. The pseudo-code of function dfs(v): // ls[v]: list of children of vertex v // its i-th element is ls[v][i]// its size is size(ls[v])sequence result = empty sequence;void dfs(vertex now){ add now to end of result; for(int i = 1; i <= size(ls[v]); i = i + 1) //loop from i = 1 to i = size(ls[v]) dfs(ls[v][i]);}InputThe first line of input contains two space-separated integers n, m (2 ≤ n ≤ 105; 1 ≤ m ≤ 105), the number of vertices of T and number of queries to perform.The i-th of the following n lines contains an integer li (0 ≤ li ≤ n), number of i-th vertex's children. Then li space-separated integers follow, the j-th of them is the index of j-th child of i-th vertex. Note that the order of these vertices is important.Each of the following m lines has one of the following format: "1 v u", "2 v h", or "3 k". The first number in the line is the type of query to perform according to the problem statement. The next numbers are description of the query.It's guaranteed that all the queries are correct. For example, in the second-type query h is at least 2 and at most distance of v from root. Also in the third-type query there is at least one vertex with distance k from the root at the time the query is given.OutputFor each query of the first or third type output one line containing the result of the query.ExamplesInput4 91 21 31 401 1 42 4 21 3 43 13 22 3 21 1 23 13 2Output3224134Input2 21 201 2 13 1Output12	Input4 91 21 31 401 1 42 4 21 3 43 13 22 3 21 1 23 13 2	Output3224134	4 seconds	512 megabytes	['data structures', '*3200']
D. Mashmokh and Water Tankstime limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard outputMashmokh is playing a new game. In the beginning he has k liters of water and p coins. Additionally he has a rooted tree (an undirected connected acyclic graph) that consists of m vertices. Each vertex of the tree contains a water tank that is empty in the beginning.The game begins with the fact that Mashmokh chooses some (no more than k) of these tanks (except the root) and pours into each of them exactly 1 liter of water. Then the following process is performed until there is no water remained in tanks. The process consists of several steps. At the beginning of each step Mashmokh opens doors of all tanks. Then Mashmokh closes doors of some tanks (he is not allowed to close door of tank in the root) for the duration of this move. Let's denote the number of liters in some tank with closed door as w, Mashmokh pays w coins for the closing of that tank during this move. Let's denote by x1, x2, ..., xm as the list of vertices of the tree sorted (nondecreasing) by their depth. The vertices from this list should be considered one by one in the order. Firstly vertex x1 (which is the root itself) is emptied. Then for each vertex xi (i > 1), if its door is closed then skip the vertex else move all the water from the tank of vertex xi to the tank of its father (even if the tank of the father is closed). Suppose l moves were made until the tree became empty. Let's denote the amount of water inside the tank of the root after the i-th move by wi then Mashmokh will win max(w1, w2, ..., wl) dollars. Mashmokh wanted to know what is the maximum amount of dollars he can win by playing the above game. He asked you to find this value for him.InputThe first line of the input contains three space-separated integers m, k, p (2 ≤ m ≤ 105; 0 ≤ k, p ≤ 109). Each of the following m - 1 lines contains two space-separated integers ai, bi (1 ≤ ai, bi ≤ m; ai ≠ bi) — the edges of the tree.Consider that the vertices of the tree are numbered from 1 to m. The root of the tree has number 1.OutputOutput a single integer, the number Mashmokh asked you to find.ExamplesInput10 2 11 21 33 43 52 66 86 79 88 10Output2Input5 1000 10001 21 33 43 5Output4NoteThe tree in the first sample is shown on the picture below. The black, red, blue colors correspond to vertices with 0, 1, 2 liters of water.One way to achieve the maximum amount of money is to put 1 liter of water in each of vertices 3 and 4. The beginning state is shown on the picture below.Then in the first move Mashmokh will pay one token to close the door of the third vertex tank. The tree after the first move is shown on the picture below.After the second move there are 2 liters of water in the root as shown on the picture below.	Input10 2 11 21 33 43 52 66 86 79 88 10	Output2	1 second	512 megabytes	['binary search', 'data structures', 'greedy', 'trees', 'two pointers', '*2300']
C. Mashmokh and Reverse Operationtime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputMashmokh's boss, Bimokh, didn't like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh's team. In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn't able to solve them. That's why he asked you to help him with these tasks. One of these tasks is the following.You have an array a of length 2n and m queries on it. The i-th query is described by an integer qi. In order to perform the i-th query you must: split the array into 2n - qi parts, where each part is a subarray consisting of 2qi numbers; the j-th subarray (1 ≤ j ≤ 2n - qi) should contain the elements a[(j - 1)·2qi + 1], a[(j - 1)·2qi + 2], ..., a[(j - 1)·2qi + 2qi]; reverse each of the subarrays; join them into a single array in the same order (this array becomes new array a); output the number of inversions in the new a. Given initial array a and all the queries. Answer all the queries. Please, note that the changes from some query is saved for further queries.InputThe first line of input contains a single integer n (0 ≤ n ≤ 20). The second line of input contains 2n space-separated integers a[1], a[2], ..., a[2n] (1 ≤ a[i] ≤ 109), the initial array.The third line of input contains a single integer m (1 ≤ m ≤ 106). The fourth line of input contains m space-separated integers q1, q2, ..., qm (0 ≤ qi ≤ n), the queries.Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.OutputOutput m lines. In the i-th line print the answer (the number of inversions) for the i-th query.ExamplesInput22 1 4 341 2 0 2Output0660Input11 230 1 1Output010NoteIf we reverse an array x[1], x[2], ..., x[n] it becomes new array y[1], y[2], ..., y[n], where y[i] = x[n - i + 1] for each i.The number of inversions of an array x[1], x[2], ..., x[n] is the number of pairs of indices i, j such that: i < j and x[i] > x[j].	Input22 1 4 341 2 0 2	Output0660	4 seconds	512 megabytes	['combinatorics', 'divide and conquer', '*2100']
B. Mashmokh and ACMtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputMashmokh's boss, Bimokh, didn't like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh's team. In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn't able to solve them. That's why he asked you to help him with these tasks. One of these tasks is the following.A sequence of l integers b1, b2, ..., bl (1 ≤ b1 ≤ b2 ≤ ... ≤ bl ≤ n) is called good if each number divides (without a remainder) by the next number in the sequence. More formally for all i (1 ≤ i ≤ l - 1).Given n and k find the number of good sequences of length k. As the answer can be rather large print it modulo 1000000007 (109 + 7).InputThe first line of input contains two space-separated integers n, k (1 ≤ n, k ≤ 2000).OutputOutput a single integer — the number of good sequences of length k modulo 1000000007 (109 + 7).ExamplesInput3 2Output5Input6 4Output39Input2 1Output2NoteIn the first sample the good sequences are: [1, 1], [2, 2], [3, 3], [1, 2], [1, 3].	Input3 2	Output5	1 second	256 megabytes	['combinatorics', 'dp', 'number theory', '*1400']
A. Mashmokh and Numberstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIt's holiday. Mashmokh and his boss, Bimokh, are playing a game invented by Mashmokh. In this game Mashmokh writes sequence of n distinct integers on the board. Then Bimokh makes several (possibly zero) moves. On the first move he removes the first and the second integer from from the board, on the second move he removes the first and the second integer of the remaining sequence from the board, and so on. Bimokh stops when the board contains less than two numbers. When Bimokh removes numbers x and y from the board, he gets gcd(x, y) points. At the beginning of the game Bimokh has zero points.Mashmokh wants to win in the game. For this reason he wants his boss to get exactly k points in total. But the guy doesn't know how choose the initial sequence in the right way. Please, help him. Find n distinct integers a1, a2, ..., an such that his boss will score exactly k points. Also Mashmokh can't memorize too huge numbers. Therefore each of these integers must be at most 109.InputThe first line of input contains two space-separated integers n, k (1 ≤ n ≤ 105; 0 ≤ k ≤ 108).OutputIf such sequence doesn't exist output -1 otherwise output n distinct space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).ExamplesInput5 2Output1 2 3 4 5Input5 3Output2 4 3 7 1Input7 2Output-1Notegcd(x, y) is greatest common divisor of x and y.	Input5 2	Output1 2 3 4 5	1 second	256 megabytes	['constructive algorithms', 'number theory', '*1500']
E. Maze 2Dtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe last product of the R2 company in the 2D games' field is a new revolutionary algorithm of searching for the shortest path in a 2 × n maze.Imagine a maze that looks like a 2 × n rectangle, divided into unit squares. Each unit square is either an empty cell or an obstacle. In one unit of time, a person can move from an empty cell of the maze to any side-adjacent empty cell. The shortest path problem is formulated as follows. Given two free maze cells, you need to determine the minimum time required to go from one cell to the other.Unfortunately, the developed algorithm works well for only one request for finding the shortest path, in practice such requests occur quite often. You, as the chief R2 programmer, are commissioned to optimize the algorithm to find the shortest path. Write a program that will effectively respond to multiple requests to find the shortest path in a 2 × n maze.InputThe first line contains two integers, n and m (1 ≤ n ≤ 2·105; 1 ≤ m ≤ 2·105) — the width of the maze and the number of queries, correspondingly. Next two lines contain the maze. Each line contains n characters, each character equals either '.' (empty cell), or 'X' (obstacle).Each of the next m lines contains two integers vi and ui (1 ≤ vi, ui ≤ 2n) — the description of the i-th request. Numbers vi, ui mean that you need to print the value of the shortest path from the cell of the maze number vi to the cell number ui. We assume that the cells of the first line of the maze are numbered from 1 to n, from left to right, and the cells of the second line are numbered from n + 1 to 2n from left to right. It is guaranteed that both given cells are empty.OutputPrint m lines. In the i-th line print the answer to the i-th request — either the size of the shortest path or -1, if we can't reach the second cell from the first one.ExamplesInput4 7.X.....X5 11 37 71 46 14 75 7Output1405222Input10 3X...X..X....X...X..X11 77 1818 10Output9-13	Input4 7.X.....X5 11 37 71 46 14 75 7	Output1405222	2 seconds	256 megabytes	['data structures', 'divide and conquer', '*2200']
D. 2048time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe programmers from the R2 company love playing 2048. One day, they decided to invent their own simplified version of this game — 2k on a stripe.Imagine an infinite in one direction stripe, consisting of unit squares (the side of each square is equal to the height of the stripe). Each square can either be empty or contain some number.Initially, all squares are empty. Then at infinity one of the unit squares number 2 or 4 appears. Then the player presses a button once, and the appeared number begins to move towards the beginning of the stripe. Let's assume that some number x moves to the beginning of the stripe, then it will stop if: it either gets in the first square of the stripe; or it is in the square that is preceded by a square with number y (y ≠ x). But if number x at some point of time gets to the square with the same number then both numbers add to each other and result in 2x. The new number 2x continues moving to the beginning of the stripe by the same rules. After the final stop of the number moving process, the infinity gets a new number 2 or 4 and the process repeats. Read the notes to the test samples to better understand the moving strategy.I guess you've understood that the game progress fully depends on the order in which numbers 2 and 4 appear. Let's look at some sequence of numbers 2 and 4 in the game. We assume that the sequence is winning if it results in at least one square getting the number greater or equal than 2k. The goal of the game is to make up a winning sequence of n numbers. But not everything is so simple, some numbers in the sequence are identified beforehand. You are given a sequence consisting of numbers 0, 2, 4. Count how many ways there are to replace each 0 of the sequence with 2 or 4 to get a winning sequence.InputThe first line contains two integers n and k (1 ≤ n ≤ 2000; 3 ≤ k ≤ 11). The next line contains sequence of n integers, each of them is either 0, or 2, or 4.OutputPrint a single integer — the number of ways to replace zeroes by numbers 2 or 4 to get a winning sequence. As this number can be rather large, print it modulo 1000000007 (109 + 7).ExamplesInput7 42 2 4 2 2 2 2Output1Input1 30Output0Input2 30 4Output1Input5 42 0 0 4 4Output2NoteConsider the first example. The beginning of the strip will look as follows: 2 → 4 → 8 → 8 2 → 8 4 → 8 4 2 → 16.To better understand the game, you can see the original game on http://gabrielecirulli.github.io/2048/. Please note that the game that is described on the strip is slightly different from the original game (when the two numbers add up in the original game, they do not keep moving). Be careful, the game is addictive, there isn't much time for the contest!	Input7 42 2 4 2 2 2 2	Output1	1 second	256 megabytes	['bitmasks', 'dp', '*2000']
C. Jeopardy!time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output'Jeopardy!' is an intellectual game where players answer questions and earn points. Company Q conducts a simplified 'Jeopardy!' tournament among the best IT companies. By a lucky coincidence, the old rivals made it to the finals: company R1 and company R2. The finals will have n questions, m of them are auction questions and n - m of them are regular questions. Each question has a price. The price of the i-th question is ai points. During the game the players chose the questions. At that, if the question is an auction, then the player who chose it can change the price if the number of his current points is strictly larger than the price of the question. The new price of the question cannot be less than the original price and cannot be greater than the current number of points of the player who chose the question. The correct answer brings the player the points equal to the price of the question. The wrong answer to the question reduces the number of the player's points by the value of the question price.The game will go as follows. First, the R2 company selects a question, then the questions are chosen by the one who answered the previous question correctly. If no one answered the question, then the person who chose last chooses again.All R2 employees support their team. They want to calculate what maximum possible number of points the R2 team can get if luck is on their side during the whole game (they will always be the first to correctly answer questions). Perhaps you are not going to be surprised, but this problem was again entrusted for you to solve.InputThe first line contains two space-separated integers n and m (1 ≤ n, m ≤ 100; m ≤ min(n, 30)) — the total number of questions and the number of auction questions, correspondingly. The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 107) — the prices of the questions. The third line contains m distinct integers bi (1 ≤ bi ≤ n) — the numbers of auction questions. Assume that the questions are numbered from 1 to n.OutputIn the single line, print the answer to the problem — the maximum points the R2 company can get if it plays optimally well. It is guaranteed that the answer fits into the integer 64-bit signed type.ExamplesInput4 11 3 7 53Output18Input3 210 3 82 3Output40Input2 2100 2001 2Output400	Input4 11 3 7 53	Output18	1 second	256 megabytes	['greedy', 'math', '*1400']
B. Spyke Chattingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe R2 company has n employees working for it. The work involves constant exchange of ideas, sharing the stories of success and upcoming challenging. For that, R2 uses a famous instant messaging program Spyke.R2 has m Spyke chats just to discuss all sorts of issues. In each chat, some group of employees exchanges messages daily. An employee can simultaneously talk in multiple chats. If some employee is in the k-th chat, he can write messages to this chat and receive notifications about messages from this chat. If an employee writes a message in the chat, all other participants of the chat receive a message notification.The R2 company is conducting an audit. Now the specialists study effective communication between the employees. For this purpose, they have a chat log and the description of chat structure. You, as one of audit specialists, are commissioned to write a program that will use this data to determine the total number of message notifications received by each employee.InputThe first line contains three space-separated integers n, m and k (2 ≤ n ≤ 2·104; 1 ≤ m ≤ 10; 1 ≤ k ≤ 2·105) — the number of the employees, the number of chats and the number of events in the log, correspondingly. Next n lines contain matrix a of size n × m, consisting of numbers zero and one. The element of this matrix, recorded in the j-th column of the i-th line, (let's denote it as aij) equals 1, if the i-th employee is the participant of the j-th chat, otherwise the element equals 0. Assume that the employees are numbered from 1 to n and the chats are numbered from 1 to m.Next k lines contain the description of the log events. The i-th line contains two space-separated integers xi and yi (1 ≤ xi ≤ n; 1 ≤ yi ≤ m) which mean that the employee number xi sent one message to chat number yi. It is guaranteed that employee number xi is a participant of chat yi. It is guaranteed that each chat contains at least two employees.OutputPrint in the single line n space-separated integers, where the i-th integer shows the number of message notifications the i-th employee receives.ExamplesInput3 4 51 1 1 11 0 1 11 1 0 01 13 11 32 43 2Output3 3 1 Input4 3 40 1 11 0 11 1 10 0 01 22 13 11 3Output0 2 3 0	Input3 4 51 1 1 11 0 1 11 1 0 01 13 11 32 43 2	Output3 3 1	1 second	256 megabytes	['implementation', '*1300']
A. Data Recoverytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputNot so long ago company R2 bought company R1 and consequently, all its developments in the field of multicore processors. Now the R2 laboratory is testing one of the R1 processors.The testing goes in n steps, at each step the processor gets some instructions, and then its temperature is measured. The head engineer in R2 is keeping a report record on the work of the processor: he writes down the minimum and the maximum measured temperature in his notebook. His assistant had to write down all temperatures into his notebook, but (for unknown reasons) he recorded only m.The next day, the engineer's assistant filed in a report with all the m temperatures. However, the chief engineer doubts that the assistant wrote down everything correctly (naturally, the chief engineer doesn't doubt his notes). So he asked you to help him. Given numbers n, m, min, max and the list of m temperatures determine whether you can upgrade the set of m temperatures to the set of n temperatures (that is add n - m temperatures), so that the minimum temperature was min and the maximum one was max.InputThe first line contains four integers n, m, min, max (1 ≤ m < n ≤ 100; 1 ≤ min < max ≤ 100). The second line contains m space-separated integers ti (1 ≤ ti ≤ 100) — the temperatures reported by the assistant.Note, that the reported temperatures, and the temperatures you want to add can contain equal temperatures.OutputIf the data is consistent, print 'Correct' (without the quotes). Otherwise, print 'Incorrect' (without the quotes).ExamplesInput2 1 1 21OutputCorrectInput3 1 1 32OutputCorrectInput2 1 1 32OutputIncorrectNoteIn the first test sample one of the possible initial configurations of temperatures is [1, 2].In the second test sample one of the possible initial configurations of temperatures is [2, 1, 3].In the third test sample it is impossible to add one temperature to obtain the minimum equal to 1 and the maximum equal to 3.	Input2 1 1 21	OutputCorrect	1 second	256 megabytes	['implementation', '*1200']
E. E-mail Addressestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputOne of the most important products of the R1 company is a popular @r1.com mail service. The R1 mailboxes receive and send millions of emails every day.Today, the online news thundered with terrible information. The R1 database crashed and almost no data could be saved except for one big string. The developers assume that the string contains the letters of some users of the R1 mail. Recovering letters is a tedious mostly manual work. So before you start this process, it was decided to estimate the difficulty of recovering. Namely, we need to calculate the number of different substrings of the saved string that form correct e-mail addresses.We assume that valid addresses are only the e-mail addresses which meet the following criteria: the address should begin with a non-empty sequence of letters, numbers, characters '_', starting with a letter; then must go character '@'; then must go a non-empty sequence of letters or numbers; then must go character '.'; the address must end with a non-empty sequence of letters. You got lucky again and the job was entrusted to you! Please note that the substring is several consecutive characters in a string. Two substrings, one consisting of the characters of the string with numbers l1, l1 + 1, l1 + 2, ..., r1 and the other one consisting of the characters of the string with numbers l2, l2 + 1, l2 + 2, ..., r2, are considered distinct if l1 ≠ l2 or r1 ≠ r2.InputThe first and the only line contains the sequence of characters s1s2... sn (1 ≤ n ≤ 106) — the saved string. It is guaranteed that the given string contains only small English letters, digits and characters '.', '_', '@'.OutputPrint in a single line the number of substrings that are valid e-mail addresses.ExamplesInput[email protected]Output18Input[email protected]@[email protected]Output8Input[email protected]Output1Input.asd123__..@Output0NoteIn the first test case all the substrings that are correct e-mail addresses begin from one of the letters of the word agapov and end in one of the letters of the word com.In the second test case note that the e-mail [email protected] is considered twice in the answer. Note that in this example the e-mail entries overlap inside the string.	Input[email protected]	Output18	1 second	256 megabytes	['implementation', '*1900']
D. Giving Awardstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe employees of the R1 company often spend time together: they watch football, they go camping, they solve contests. So, it's no big deal that sometimes someone pays for someone else.Today is the day of giving out money rewards. The R1 company CEO will invite employees into his office one by one, rewarding each one for the hard work this month. The CEO knows who owes money to whom. And he also understands that if he invites person x to his office for a reward, and then immediately invite person y, who has lent some money to person x, then they can meet. Of course, in such a situation, the joy of person x from his brand new money reward will be much less. Therefore, the R1 CEO decided to invite the staff in such an order that the described situation will not happen for any pair of employees invited one after another.However, there are a lot of employees in the company, and the CEO doesn't have a lot of time. Therefore, the task has been assigned to you. Given the debt relationships between all the employees, determine in which order they should be invited to the office of the R1 company CEO, or determine that the described order does not exist.InputThe first line contains space-separated integers n and m — the number of employees in R1 and the number of debt relations. Each of the following m lines contains two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi), these integers indicate that the person number ai owes money to a person a number bi. Assume that all the employees are numbered from 1 to n.It is guaranteed that each pair of people p, q is mentioned in the input data at most once. In particular, the input data will not contain pairs p, q and q, p simultaneously.OutputPrint -1 if the described order does not exist. Otherwise, print the permutation of n distinct integers. The first number should denote the number of the person who goes to the CEO office first, the second number denote the person who goes second and so on.If there are multiple correct orders, you are allowed to print any of them.ExamplesInput2 11 2Output2 1 Input3 31 22 33 1Output2 1 3	Input2 11 2	Output2 1	1 second	256 megabytes	['dfs and similar', '*2000']
C. Patterntime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputDevelopers often face with regular expression patterns. A pattern is usually defined as a string consisting of characters and metacharacters that sets the rules for your search. These patterns are most often used to check whether a particular string meets the certain rules.In this task, a pattern will be a string consisting of small English letters and question marks ('?'). The question mark in the pattern is a metacharacter that denotes an arbitrary small letter of the English alphabet. We will assume that a string matches the pattern if we can transform the string into the pattern by replacing the question marks by the appropriate characters. For example, string aba matches patterns: ???, ??a, a?a, aba.Programmers that work for the R1 company love puzzling each other (and themselves) with riddles. One of them is as follows: you are given n patterns of the same length, you need to find a pattern that contains as few question marks as possible, and intersects with each of the given patterns. Two patterns intersect if there is a string that matches both the first and the second pattern. Can you solve this riddle?InputThe first line contains a single integer n (1 ≤ n ≤ 105) — the number of patterns. Next n lines contain the patterns.It is guaranteed that the patterns can only consist of small English letters and symbols '?'. All patterns are non-empty and have the same length. The total length of all the patterns does not exceed 105 characters.OutputIn a single line print the answer to the problem — the pattern with the minimal number of signs '?', which intersects with each of the given ones. If there are several answers, print any of them.ExamplesInput2?ab??bOutputxabInput2abOutput?Input1?a?bOutputcacbNoteConsider the first example. Pattern xab intersects with each of the given patterns. Pattern ??? also intersects with each of the given patterns, but it contains more question signs, hence it is not an optimal answer. Clearly, xab is the optimal answer, because it doesn't contain any question sign. There are a lot of other optimal answers, for example: aab, bab, cab, dab and so on.	Input2?ab??b	Outputxab	1 second	256 megabytes	['implementation', 'strings', '*1200']
B. Network Configurationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe R1 company wants to hold a web search championship. There were n computers given for the competition, each of them is connected to the Internet. The organizers believe that the data transfer speed directly affects the result. The higher the speed of the Internet is, the faster the participant will find the necessary information. Therefore, before the competition started, each computer had its maximum possible data transfer speed measured. On the i-th computer it was ai kilobits per second.There will be k participants competing in the championship, each should get a separate computer. The organizing company does not want any of the participants to have an advantage over the others, so they want to provide the same data transfer speed to each participant's computer. Also, the organizers want to create the most comfortable conditions for the participants, so the data transfer speed on the participants' computers should be as large as possible.The network settings of the R1 company has a special option that lets you to cut the initial maximum data transfer speed of any computer to any lower speed. How should the R1 company configure the network using the described option so that at least k of n computers had the same data transfer speed and the data transfer speed on these computers was as large as possible?InputThe first line contains two space-separated integers n and k (1 ≤ k ≤ n ≤ 100) — the number of computers and the number of participants, respectively. In the second line you have a space-separated sequence consisting of n integers: a1, a2, ..., an (16 ≤ ai ≤ 32768); number ai denotes the maximum data transfer speed on the i-th computer.OutputPrint a single integer — the maximum Internet speed value. It is guaranteed that the answer to the problem is always an integer.ExamplesInput3 240 20 30Output30Input6 4100 20 40 20 50 50Output40NoteIn the first test case the organizers can cut the first computer's speed to 30 kilobits. Then two computers (the first and the third one) will have the same speed of 30 kilobits. They should be used as the participants' computers. This answer is optimal.	Input3 240 20 30	Output30	1 second	256 megabytes	['greedy', 'sortings', '*900']
A. Postertime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe R1 company has recently bought a high rise building in the centre of Moscow for its main office. It's time to decorate the new office, and the first thing to do is to write the company's slogan above the main entrance to the building.The slogan of the company consists of n characters, so the decorators hung a large banner, n meters wide and 1 meter high, divided into n equal squares. The first character of the slogan must be in the first square (the leftmost) of the poster, the second character must be in the second square, and so on.Of course, the R1 programmers want to write the slogan on the poster themselves. To do this, they have a large (and a very heavy) ladder which was put exactly opposite the k-th square of the poster. To draw the i-th character of the slogan on the poster, you need to climb the ladder, standing in front of the i-th square of the poster. This action (along with climbing up and down the ladder) takes one hour for a painter. The painter is not allowed to draw characters in the adjacent squares when the ladder is in front of the i-th square because the uncomfortable position of the ladder may make the characters untidy. Besides, the programmers can move the ladder. In one hour, they can move the ladder either a meter to the right or a meter to the left.Drawing characters and moving the ladder is very tiring, so the programmers want to finish the job in as little time as possible. Develop for them an optimal poster painting plan!InputThe first line contains two integers, n and k (1 ≤ k ≤ n ≤ 100) — the number of characters in the slogan and the initial position of the ladder, correspondingly. The next line contains the slogan as n characters written without spaces. Each character of the slogan is either a large English letter, or digit, or one of the characters: '.', '!', ',', '?'.OutputIn t lines, print the actions the programmers need to make. In the i-th line print: "LEFT" (without the quotes), if the i-th action was "move the ladder to the left"; "RIGHT" (without the quotes), if the i-th action was "move the ladder to the right"; "PRINT x" (without the quotes), if the i-th action was to "go up the ladder, paint character x, go down the ladder". The painting time (variable t) must be minimum possible. If there are multiple optimal painting plans, you can print any of them.ExamplesInput2 2R1OutputPRINT 1LEFTPRINT RInput2 1R1OutputPRINT RRIGHTPRINT 1Input6 4GO?GO!OutputRIGHTRIGHTPRINT !LEFTPRINT OLEFTPRINT GLEFTPRINT ?LEFTPRINT OLEFTPRINT GNoteNote that the ladder cannot be shifted by less than one meter. The ladder can only stand in front of some square of the poster. For example, you cannot shift a ladder by half a meter and position it between two squares. Then go up and paint the first character and the second character.	Input2 2R1	OutputPRINT 1LEFTPRINT R	1 second	256 megabytes	['greedy', 'implementation', '*900']
C. Kickertime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputKicker (table football) is a board game based on football, in which players control the footballers' figures mounted on rods by using bars to get the ball into the opponent's goal. When playing two on two, one player of each team controls the goalkeeper and the full-backs (plays defence), the other player controls the half-backs and forwards (plays attack).Two teams of company Q decided to battle each other. Let's enumerate players from both teams by integers from 1 to 4. The first and second player play in the first team, the third and the fourth one play in the second team. For each of the four players we know their game skills in defence and attack. The defence skill of the i-th player is ai, the attack skill is bi.Before the game, the teams determine how they will play. First the players of the first team decide who will play in the attack, and who will play in the defence. Then the second team players do the same, based on the choice of their opponents.We will define a team's defence as the defence skill of player of the team who plays defence. Similarly, a team's attack is the attack skill of the player of the team who plays attack. We assume that one team is guaranteed to beat the other one, if its defence is strictly greater than the opponent's attack and its attack is strictly greater than the opponent's defence.The teams of company Q know each other's strengths and therefore arrange their teams optimally. Identify the team that is guaranteed to win (if both teams act optimally) or tell that there is no such team.InputThe input contain the players' description in four lines. The i-th line contains two space-separated integers ai and bi (1 ≤ ai, bi ≤ 100) — the defence and the attack skill of the i-th player, correspondingly.OutputIf the first team can win, print phrase "Team 1" (without the quotes), if the second team can win, print phrase "Team 2" (without the quotes). If no of the teams can definitely win, print "Draw" (without the quotes).ExamplesInput1 100100 199 9999 99OutputTeam 1Input1 12 23 32 2OutputTeam 2Input3 32 21 12 2OutputDrawNoteLet consider the first test sample. The first team can definitely win if it will choose the following arrangement: the first player plays attack, the second player plays defence.Consider the second sample. The order of the choosing roles for players makes sense in this sample. As the members of the first team choose first, the members of the second team can beat them (because they know the exact defence value and attack value of the first team).	Input1 100100 199 9999 99	OutputTeam 1	1 second	256 megabytes	['implementation', '*1700']
B. Multi-core Processortime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe research center Q has developed a new multi-core processor. The processor consists of n cores and has k cells of cache memory. Consider the work of this processor.At each cycle each core of the processor gets one instruction: either do nothing, or the number of the memory cell (the core will write an information to the cell). After receiving the command, the core executes it immediately. Sometimes it happens that at one cycle, multiple cores try to write the information into a single cell. Unfortunately, the developers did not foresee the possibility of resolving conflicts between cores, so in this case there is a deadlock: all these cores and the corresponding memory cell are locked forever. Each of the locked cores ignores all further commands, and no core in the future will be able to record an information into the locked cell. If any of the cores tries to write an information into some locked cell, it is immediately locked.The development team wants to explore the deadlock situation. Therefore, they need a program that will simulate the processor for a given set of instructions for each core within m cycles . You're lucky, this interesting work is entrusted to you. According to the instructions, during the m cycles define for each core the number of the cycle, during which it will become locked. It is believed that initially all cores and all memory cells are not locked.InputThe first line contains three integers n, m, k (1 ≤ n, m, k ≤ 100). Then follow n lines describing instructions. The i-th line contains m integers: xi1, xi2, ..., xim (0 ≤ xij ≤ k), where xij is the instruction that must be executed by the i-th core at the j-th cycle. If xij equals 0, then the corresponding instruction is «do nothing». But if xij is a number from 1 to k, then the corresponding instruction is «write information to the memory cell number xij».We assume that the cores are numbered from 1 to n, the work cycles are numbered from 1 to m and the memory cells are numbered from 1 to k.OutputPrint n lines. In the i-th line print integer ti. This number should be equal to 0 if the i-th core won't be locked, or it should be equal to the number of the cycle when this core will be locked.ExamplesInput4 3 51 0 01 0 22 3 13 2 0Output1130Input3 2 21 21 22 2Output110Input1 1 10Output0	Input4 3 51 0 01 0 22 3 13 2 0	Output1130	1 second	256 megabytes	['implementation', '*1600']
A. Password Checktime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou have probably registered on Internet sites many times. And each time you should enter your invented password. Usually the registration form automatically checks the password's crypt resistance. If the user's password isn't complex enough, a message is displayed. Today your task is to implement such an automatic check.Web-developers of the company Q assume that a password is complex enough, if it meets all of the following conditions: the password length is at least 5 characters; the password contains at least one large English letter; the password contains at least one small English letter; the password contains at least one digit. You are given a password. Please implement the automatic check of its complexity for company Q.InputThe first line contains a non-empty sequence of characters (at most 100 characters). Each character is either a large English letter, or a small English letter, or a digit, or one of characters: "!", "?", ".", ",", "_".OutputIf the password is complex enough, print message "Correct" (without the quotes), otherwise print message "Too weak" (without the quotes).ExamplesInputabacabaOutputToo weakInputX12345OutputToo weakInputCONTEST_is_STARTED!!11OutputCorrect	Inputabacaba	OutputToo weak	1 second	256 megabytes	['special problem', 'implementation', '800']
I. Feed the Golorptime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputGolorps are mysterious creatures who feed on variables. Golorp's name is a program in some programming language. Some scientists believe that this language is Befunge; golorps are tantalizingly silent.Variables consumed by golorps can take values from 0 to 9, inclusive. For each golorp its daily diet is defined by its name. Some golorps are so picky that they can't be fed at all. Besides, all golorps are very health-conscious and try to eat as little as possible. Given a choice of several valid sequences of variable values, each golorp will choose lexicographically smallest one.For the purposes of this problem you can assume that a golorp consists of jaws and a stomach. The number of variables necessary to feed a golorp is defined by the shape of its jaws. Variables can get to the stomach only via the jaws.A hungry golorp is visiting you. You know its name; feed it or figure out that it's impossible.InputThe input is a single string (between 13 and 1024 characters long) — the name of the visiting golorp. All names are similar and will resemble the ones given in the samples. The name is guaranteed to be valid.OutputOutput lexicographically smallest sequence of variable values fit for feeding this golorp. Values should be listed in the order in which they get into the jaws. If the golorp is impossible to feed, output "false".ExamplesInput?(_-_/_____):-___>__.Output0010Input?(__-_+_/_____):-__>__,_____<__.OutputfalseInput?(______________________/____+_________-_____*______-___):-__<___,___<____,____<_____,_____<______,______<_______.Output0250341Input?(__+___+__-___):-___>__.Output0101	Input?(_-_/___*__):-___>__.	Output0010	1 second	256 megabytes	['special problem', '2400']
H. A + B Strikes Backtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA + B is often used as an example of the easiest problem possible to show some contest platform. However, some scientists have observed that sometimes this problem is not so easy to get accepted. Want to try?InputThe input contains two integers a and b (0 ≤ a, b ≤ 103), separated by a single space.OutputOutput the sum of the given integers.ExamplesInput5 14Output19Input381 492Output873	Input5 14	Output19	1 second	256 megabytes	['special problem', 'brute force', 'constructive algorithms', 'dsu', 'implementation', '1500']
G. On a planetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputInputThe first line contains a single integer n (1 ≤ n ≤ 1000) — the number of points on a plane.Each of the next n lines contains two real coordinates xi and yi of the point, specified with exactly 2 fractional digits. All coordinates are between - 1000 and 1000, inclusive.OutputOutput a single real number θ — the answer to the problem statement. The absolute or relative error of your answer should be at most 10 - 2.ExamplesInput8-2.14 2.06-1.14 2.04-2.16 1.46-2.14 0.70-1.42 0.40-0.94 -0.48-1.42 -1.28-2.16 -1.62Output5.410Input52.26 1.442.28 0.642.30 -0.301.58 0.663.24 0.66Output5.620Input86.98 2.066.40 1.125.98 0.245.54 -0.607.16 0.307.82 1.248.34 0.248.74 -0.76Output5.480Input510.44 2.0610.90 0.8011.48 -0.4812.06 0.7612.54 2.06Output6.040Input816.94 2.4215.72 2.3814.82 1.5814.88 0.5015.76 -0.1616.86 -0.2017.00 0.8816.40 0.92Output6.040Input720.62 3.0021.06 2.2821.56 1.3621.66 0.5621.64 -0.5222.14 2.3222.62 3.04Output6.720	Input8-2.14 2.06-1.14 2.04-2.16 1.46-2.14 0.70-1.42 0.40-0.94 -0.48-1.42 -1.28-2.16 -1.62	Output5.410	1 second	256 megabytes	['special problem', 'geometry', '2200']
F. 000001time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputInputThe input contains a single integer a (1 ≤ a ≤ 64).OutputOutput a single integer.ExamplesInput2Output1Input4Output2Input27Output5Input42Output6	Input2	Output1	1 second	256 megabytes	['special problem', '1900']
E. Dometime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output InputThe input contains a single floating-point number x with exactly 6 decimal places (0 < x < 5).OutputOutput two integers separated by a single space. Each integer should be between 1 and 10, inclusive. If several solutions exist, output any of them. Solution will exist for all tests.ExamplesInput1.200000Output3 2Input2.572479Output10 3Input4.024922Output9 9	Input1.200000	Output3 2	1 second	256 megabytes	['special problem', '1800']
D. Big Datatime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Petya wanted to give an April Fools Day present to some scientists. After some hesitation he decided to give them the array that he got as a present in Codeforces Round #153 (Div.2). The scientists rejoiced at the gift and decided to put some important facts to this array. Here are the first few of the facts: The highest mountain above sea level in the world is Mount Everest. Its peak rises to 8848 m. The largest board game tournament consisted of 958 participants playing chapaev. The largest online maths competition consisted of 12766 participants. The Nile is credited as the longest river in the world. From its farthest stream in Burundi, it extends 6695 km in length. While not in flood, the main stretches of the Amazon river in South America can reach widths of up to 1100 km at its widest points. Angel Falls is the highest waterfall. Its greatest single drop measures 807 m. The Hotel Everest View above Namche, Nepal — the village closest to Everest base camp – is at a record height of 31962 m Uranium is the heaviest of all the naturally occurring elements. Its most common isotope has a nucleus containing 146 neutrons. The coldest permanently inhabited place is the Siberian village of Oymyakon, where the temperature of -68°C was registered in the twentieth century. The longest snake held in captivity is over 25 feet long. Its name is Medusa. Colonel Meow holds the world record for longest fur on a cat — almost 134 centimeters. Sea otters can have up to 10000 hairs per square inch. This is the most dense fur in the animal kingdom. The largest state of USA is Alaska; its area is 663268 square miles Alaska has a longer coastline than all of the other 49 U.S. States put together: it is 154103 miles long. Lake Baikal is the largest freshwater lake in the world. It reaches 1642 meters in depth and contains around one-fifth of the world’s unfrozen fresh water. The most colorful national flag is the one of Turkmenistan, with 106 colors. InputThe input will contain a single integer between 1 and 16.OutputOutput a single integer.ExamplesInput1Output1Input7Output0	Input1	Output1	1 second	256 megabytes	['special problem', '1700']
C. Magnum Opustime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputSalve, mi amice.Et tu quidem de lapis philosophorum. Barba non facit philosophum. Labor omnia vincit. Non potest creatio ex nihilo. Necesse est partibus.Rp: I Aqua Fortis I Aqua Regia II Amalgama VII Minium IV VitriolMisce in vitro et æstus, et nil admirari. Festina lente, et nulla tenaci invia est via.Fac et spera,Vale,Nicolas FlamelInputThe first line of input contains several space-separated integers ai (0 ≤ ai ≤ 100).OutputPrint a single integer.ExamplesInput2 4 6 8 10Output1	Input2 4 6 8 10	Output1	1 second	256 megabytes	['special problem', '1700']
A. The Great Gametime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputTwo teams meet in The Game World Championship. Some scientists consider this game to be the most intellectually challenging game in the world. You are given two strings describing the teams' actions in the final battle. Figure out who became the champion.InputThe input contains two strings of equal length (between 2 and 20 characters, inclusive). Each line describes the actions of one team.OutputOutput "TEAM 1 WINS" if the first team won, "TEAM 2 WINS" if the second team won, and "TIE" if there was a tie.ExamplesInput[]()[]8<8<[]()8<OutputTEAM 2 WINSInput8<8<()[]8<[]OutputTIE	Input[]()[]8<8<[]()8<	OutputTEAM 2 WINS	1 second	256 megabytes	['special problem', '1700']
B. Garlandtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputOnce little Vasya read an article in a magazine on how to make beautiful handmade garland from colored paper. Vasya immediately went to the store and bought n colored sheets of paper, the area of each sheet is 1 square meter.The garland must consist of exactly m pieces of colored paper of arbitrary area, each piece should be of a certain color. To make the garland, Vasya can arbitrarily cut his existing colored sheets into pieces. Vasya is not obliged to use all the sheets to make the garland.Vasya wants the garland to be as attractive as possible, so he wants to maximize the total area of m pieces of paper in the garland. Calculate what the maximum total area of the pieces of paper in the garland Vasya can get.InputThe first line contains a non-empty sequence of n (1 ≤ n ≤ 1000) small English letters ("a"..."z"). Each letter means that Vasya has a sheet of paper of the corresponding color.The second line contains a non-empty sequence of m (1 ≤ m ≤ 1000) small English letters that correspond to the colors of the pieces of paper in the garland that Vasya wants to make.OutputPrint an integer that is the maximum possible total area of the pieces of paper in the garland Vasya wants to get or -1, if it is impossible to make the garland from the sheets he's got. It is guaranteed that the answer is always an integer.ExamplesInputaaabbacaabbccacOutput6InputazOutput-1NoteIn the first test sample Vasya can make an garland of area 6: he can use both sheets of color b, three (but not four) sheets of color a and cut a single sheet of color c in three, for example, equal pieces. Vasya can use the resulting pieces to make a garland of area 6.In the second test sample Vasya cannot make a garland at all — he doesn't have a sheet of color z.	Inputaaabbacaabbccac	Output6	1 second	256 megabytes	['implementation', '*1200']
A. Line to Cashiertime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Vasya went to the supermarket to get some groceries. He walked about the supermarket for a long time and got a basket full of products. Now he needs to choose the cashier to pay for the products.There are n cashiers at the exit from the supermarket. At the moment the queue for the i-th cashier already has ki people. The j-th person standing in the queue to the i-th cashier has mi, j items in the basket. Vasya knows that: the cashier needs 5 seconds to scan one item; after the cashier scans each item of some customer, he needs 15 seconds to take the customer's money and give him the change. Of course, Vasya wants to select a queue so that he can leave the supermarket as soon as possible. Help him write a program that displays the minimum number of seconds after which Vasya can get to one of the cashiers.InputThe first line contains integer n (1 ≤ n ≤ 100) — the number of cashes in the shop. The second line contains n space-separated integers: k1, k2, ..., kn (1 ≤ ki ≤ 100), where ki is the number of people in the queue to the i-th cashier.The i-th of the next n lines contains ki space-separated integers: mi, 1, mi, 2, ..., mi, ki (1 ≤ mi, j ≤ 100) — the number of products the j-th person in the queue for the i-th cash has.OutputPrint a single integer — the minimum number of seconds Vasya needs to get to the cashier.ExamplesInput111Output20Input41 4 3 21001 2 2 31 9 17 8Output100NoteIn the second test sample, if Vasya goes to the first queue, he gets to the cashier in 100·5 + 15 = 515 seconds. But if he chooses the second queue, he will need 1·5 + 2·5 + 2·5 + 3·5 + 4·15 = 100 seconds. He will need 1·5 + 9·5 + 1·5 + 3·15 = 100 seconds for the third one and 7·5 + 8·5 + 2·15 = 105 seconds for the fourth one. Thus, Vasya gets to the cashier quicker if he chooses the second or the third queue.	Input111	Output20	1 second	256 megabytes	['implementation', '*900']
E. k-d-sequencetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputWe'll call a sequence of integers a good k-d sequence if we can add to it at most k numbers in such a way that after the sorting the sequence will be an arithmetic progression with difference d.You got hold of some sequence a, consisting of n integers. Your task is to find its longest contiguous subsegment, such that it is a good k-d sequence.InputThe first line contains three space-separated integers n, k, d (1 ≤ n ≤ 2·105; 0 ≤ k ≤ 2·105; 0 ≤ d ≤ 109). The second line contains n space-separated integers: a1, a2, ..., an ( - 109 ≤ ai ≤ 109) — the actual sequence.OutputPrint two space-separated integers l, r (1 ≤ l ≤ r ≤ n) show that sequence al, al + 1, ..., ar is the longest subsegment that is a good k-d sequence.If there are multiple optimal answers, print the one with the minimum value of l.ExamplesInput6 1 24 3 2 8 6 2Output3 5NoteIn the first test sample the answer is the subsegment consisting of numbers 2, 8, 6 — after adding number 4 and sorting it becomes sequence 2, 4, 6, 8 — the arithmetic progression with difference 2.	Input6 1 24 3 2 8 6 2	Output3 5	2 seconds	256 megabytes	['data structures', '*3100']
D. Largest Submatrix 3time limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given matrix a of size n × m, its elements are integers. We will assume that the rows of the matrix are numbered from top to bottom from 1 to n, the columns are numbered from left to right from 1 to m. We will denote the element on the intersecting of the i-th row and the j-th column as aij.We'll call submatrix i1, j1, i2, j2 (1 ≤ i1 ≤ i2 ≤ n; 1 ≤ j1 ≤ j2 ≤ m) such elements aij of the given matrix that i1 ≤ i ≤ i2 AND j1 ≤ j ≤ j2. We'll call the area of the submatrix number (i2 - i1 + 1)·(j2 - j1 + 1). We'll call a submatrix inhomogeneous, if all its elements are distinct.Find the largest (in area) inhomogenous submatrix of the given matrix.InputThe first line contains two integers n, m (1 ≤ n, m ≤ 400) — the number of rows and columns of the matrix, correspondingly.Each of the next n lines contains m integers aij (1 ≤ aij ≤ 160000) — the elements of the matrix.OutputPrint a single integer — the area of the optimal inhomogenous submatrix.ExamplesInput3 31 3 14 5 62 6 1Output6Input3 45 2 3 13 3 5 34 4 4 5Output4Input2 61 2 3 4 5 68 6 7 8 9 1Output8	Input3 31 3 14 5 62 6 1	Output6	3 seconds	256 megabytes	['dp', 'hashing', '*2700']
C. Curious Arraytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou've got an array consisting of n integers: a[1], a[2], ..., a[n]. Moreover, there are m queries, each query can be described by three integers li, ri, ki. Query li, ri, ki means that we should add to each element a[j], where li ≤ j ≤ ri.Record means the binomial coefficient, or the number of combinations from y elements into groups of x elements.You need to fulfil consecutively all queries and then print the final array.InputThe first line contains integers n, m (1 ≤ n, m ≤ 105).The second line contains n integers a[1], a[2], ..., a[n] (0 ≤ ai ≤ 109) — the initial array.Next m lines contain queries in the format li, ri, ki — to all elements of the segment li... ri add number (1 ≤ li ≤ ri ≤ n; 0 ≤ k ≤ 100).OutputPrint n integers: the i-th number is the value of element a[i] after all the queries. As the values can be rather large, print them modulo 1000000007 (109 + 7).ExamplesInput5 10 0 0 0 01 5 0Output1 1 1 1 1Input10 21 2 3 4 5 0 0 0 0 01 6 16 10 2Output2 4 6 8 10 7 3 6 10 15	Input5 10 0 0 0 01 5 0	Output1 1 1 1 1	2 seconds	256 megabytes	['brute force', 'combinatorics', 'implementation', 'math', '*2500']
B. Long Pathtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputOne day, little Vasya found himself in a maze consisting of (n + 1) rooms, numbered from 1 to (n + 1). Initially, Vasya is at the first room and to get out of the maze, he needs to get to the (n + 1)-th one.The maze is organized as follows. Each room of the maze has two one-way portals. Let's consider room number i (1 ≤ i ≤ n), someone can use the first portal to move from it to room number (i + 1), also someone can use the second portal to move from it to room number pi, where 1 ≤ pi ≤ i.In order not to get lost, Vasya decided to act as follows. Each time Vasya enters some room, he paints a cross on its ceiling. Initially, Vasya paints a cross at the ceiling of room 1. Let's assume that Vasya is in room i and has already painted a cross on its ceiling. Then, if the ceiling now contains an odd number of crosses, Vasya uses the second portal (it leads to room pi), otherwise Vasya uses the first portal. Help Vasya determine the number of times he needs to use portals to get to room (n + 1) in the end.InputThe first line contains integer n (1 ≤ n ≤ 103) — the number of rooms. The second line contains n integers pi (1 ≤ pi ≤ i). Each pi denotes the number of the room, that someone can reach, if he will use the second portal in the i-th room.OutputPrint a single number — the number of portal moves the boy needs to go out of the maze. As the number can be rather large, print it modulo 1000000007 (109 + 7).ExamplesInput21 2Output4Input41 1 2 3Output20Input51 1 1 1 1Output62	Input21 2	Output4	1 second	256 megabytes	['dp', 'implementation', '*1600']
A. Triangletime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.InputThe first line contains two integers a, b (1 ≤ a, b ≤ 1000), separated by a single space.OutputIn the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers — the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.ExamplesInput1 1OutputNOInput5 5OutputYES2 15 5-2 4Input5 10OutputYES-10 4-2 -21 2	Input1 1	OutputNO	1 second	256 megabytes	['brute force', 'geometry', 'implementation', 'math', '*1600']
E. Hamming Triplestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Chris is having a nightmare. Even in dreams all he thinks about is math.Chris dreams about m binary strings of length n, indexed with numbers from 1 to m. The most horrifying part is that the bits of each string are ordered in either ascending or descending order. For example, Chris could be dreaming about the following 4 strings of length 5: The Hamming distance H(a, b) between two strings a and b of length n is the number of positions at which the corresponding symbols are different. Сhris thinks that each three strings with different indices constitute a single triple. Chris's delusion is that he will wake up only if he counts the number of such string triples a, b, c that the sum H(a, b) + H(b, c) + H(c, a) is maximal among all the string triples constructed from the dreamed strings.Help Chris wake up from this nightmare!InputThe first line of input contains two space-separated integers n and m (1 ≤ n ≤ 109; 3 ≤ m ≤ 105), the length and the number of strings. The next m lines contain the description of the strings. The i-th line contains two space-separated integers si and fi (0 ≤ si ≤ 1; 1 ≤ fi ≤ n), the description of the string with index i; that means that the first fi bits of the i-th string are equal to si, and the remaining n - fi bits are equal to 1 - si. There can be multiple equal strings in Chris's dream.OutputOutput a single integer, the number of such string triples among the given that the sum of the Hamming distances between the strings of the triple is maximal.ExamplesInput5 40 30 51 41 5Output3Input10 41 50 50 51 5Output4	Input5 40 30 51 41 5	Output3	1 second	256 megabytes	['implementation', 'math', 'two pointers', '*2800']
D. Hill Climbingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis problem has nothing to do with Little Chris. It is about hill climbers instead (and Chris definitely isn't one).There are n hills arranged on a line, each in the form of a vertical line segment with one endpoint on the ground. The hills are numbered with numbers from 1 to n from left to right. The i-th hill stands at position xi with its top at height yi. For every two hills a and b, if the top of hill a can be seen from the top of hill b, their tops are connected by a rope. Formally, the tops of two hills are connected if the segment connecting their top points does not intersect or touch any of the other hill segments. Using these ropes, the hill climbers can move from hill to hill.There are m teams of climbers, each composed of exactly two members. The first and the second climbers of the i-th team are located at the top of the ai-th and bi-th hills, respectively. They want to meet together at the top of some hill. Now, each of two climbers move according to the following process: if a climber is at the top of the hill where the other climber is already located or will come eventually, the former climber stays at this hill; otherwise, the climber picks a hill to the right of his current hill that is reachable by a rope and is the rightmost possible, climbs this hill and continues the process (the climber can also climb a hill whose top is lower than the top of his current hill). For each team of climbers, determine the number of the meeting hill for this pair!InputThe first line of input contains a single integer n (1 ≤ n ≤ 105), the number of hills. The next n lines describe the hills. The i-th of them contains two space-separated integers xi, yi (1 ≤ xi ≤ 107; 1 ≤ yi ≤ 1011), the position and the height of the i-th hill. The hills are given in the ascending order of xi, i.e., xi < xj for i < j.The next line of input contains a single integer m (1 ≤ m ≤ 105), the number of teams. The next m lines describe the teams. The i-th of them contains two space-separated integers ai, bi (1 ≤ ai, bi ≤ n), the numbers of the hills where the climbers of the i-th team are located. It is possible that ai = bi.OutputIn a single line output m space-separated integers, where the i-th integer is the number of the meeting hill for the members of the i-th team.ExamplesInput61 42 13 24 36 47 433 15 62 3Output5 6 3	Input61 42 13 24 36 47 433 15 62 3	Output5 6 3	1 second	256 megabytes	['dfs and similar', 'geometry', 'trees', '*2200']
E. Graph Cuttingtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Chris is participating in a graph cutting contest. He's a pro. The time has come to test his skills to the fullest.Chris is given a simple undirected connected graph with n vertices (numbered from 1 to n) and m edges. The problem is to cut it into edge-distinct paths of length 2. Formally, Chris has to partition all edges of the graph into pairs in such a way that the edges in a single pair are adjacent and each edge must be contained in exactly one pair.For example, the figure shows a way Chris can cut a graph. The first sample test contains the description of this graph. You are given a chance to compete with Chris. Find a way to cut the given graph or determine that it is impossible!InputThe first line of input contains two space-separated integers n and m (1 ≤ n, m ≤ 105), the number of vertices and the number of edges in the graph. The next m lines contain the description of the graph's edges. The i-th line contains two space-separated integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi), the numbers of the vertices connected by the i-th edge. It is guaranteed that the given graph is simple (without self-loops and multi-edges) and connected.Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.OutputIf it is possible to cut the given graph into edge-distinct paths of length 2, output lines. In the i-th line print three space-separated integers xi, yi and zi, the description of the i-th path. The graph should contain this path, i.e., the graph should contain edges (xi, yi) and (yi, zi). Each edge should appear in exactly one path of length 2. If there are multiple solutions, output any of them.If it is impossible to cut the given graph, print "No solution" (without quotes).ExamplesInput8 121 22 33 44 11 32 43 53 65 66 76 87 8Output1 2 41 3 21 4 35 3 65 6 86 7 8Input3 31 22 33 1OutputNo solutionInput3 21 22 3Output1 2 3	Input8 121 22 33 44 11 32 43 53 65 66 76 87 8	Output1 2 41 3 21 4 35 3 65 6 86 7 8	2 seconds	256 megabytes	['dfs and similar', 'graphs', '*2300']
D. Toy Sumtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Chris is very keen on his toy blocks. His teacher, however, wants Chris to solve more problems, so he decided to play a trick on Chris.There are exactly s blocks in Chris's set, each block has a unique number from 1 to s. Chris's teacher picks a subset of blocks X and keeps it to himself. He will give them back only if Chris can pick such a non-empty subset Y from the remaining blocks, that the equality holds: "Are you kidding me?", asks Chris.For example, consider a case where s = 8 and Chris's teacher took the blocks with numbers 1, 4 and 5. One way for Chris to choose a set is to pick the blocks with numbers 3 and 6, see figure. Then the required sums would be equal: (1 - 1) + (4 - 1) + (5 - 1) = (8 - 3) + (8 - 6) = 7. However, now Chris has exactly s = 106 blocks. Given the set X of blocks his teacher chooses, help Chris to find the required set Y!InputThe first line of input contains a single integer n (1 ≤ n ≤ 5·105), the number of blocks in the set X. The next line contains n distinct space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 106), the numbers of the blocks in X.Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.OutputIn the first line of output print a single integer m (1 ≤ m ≤ 106 - n), the number of blocks in the set Y. In the next line output m distinct space-separated integers y1, y2, ..., ym (1 ≤ yi ≤ 106), such that the required equality holds. The sets X and Y should not intersect, i.e. xi ≠ yj for all i, j (1 ≤ i ≤ n; 1 ≤ j ≤ m). It is guaranteed that at least one solution always exists. If there are multiple solutions, output any of them.ExamplesInput31 4 5Output2999993 1000000Input11Output11000000	Input31 4 5	Output2999993 1000000	1 second	256 megabytes	['greedy', 'implementation', 'math', '*1700']
C. Unusual Producttime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Chris is a huge fan of linear algebra. This time he has been given a homework about the unusual square of a square matrix.The dot product of two integer number vectors x and y of size n is the sum of the products of the corresponding components of the vectors. The unusual square of an n × n square matrix A is defined as the sum of n dot products. The i-th of them is the dot product of the i-th row vector and the i-th column vector in the matrix A.Fortunately for Chris, he has to work only in GF(2)! This means that all operations (addition, multiplication) are calculated modulo 2. In fact, the matrix A is binary: each element of A is either 0 or 1. For example, consider the following matrix A: The unusual square of A is equal to (1·1 + 1·0 + 1·1) + (0·1 + 1·1 + 1·0) + (1·1 + 0·1 + 0·0) = 0 + 1 + 1 = 0.However, there is much more to the homework. Chris has to process q queries; each query can be one of the following: given a row index i, flip all the values in the i-th row in A; given a column index i, flip all the values in the i-th column in A; find the unusual square of A. To flip a bit value w means to change it to 1 - w, i.e., 1 changes to 0 and 0 changes to 1.Given the initial matrix A, output the answers for each query of the third type! Can you solve Chris's homework?InputThe first line of input contains an integer n (1 ≤ n ≤ 1000), the number of rows and the number of columns in the matrix A. The next n lines describe the matrix: the i-th line contains n space-separated bits and describes the i-th row of A. The j-th number of the i-th line aij (0 ≤ aij ≤ 1) is the element on the intersection of the i-th row and the j-th column of A.The next line of input contains an integer q (1 ≤ q ≤ 106), the number of queries. Each of the next q lines describes a single query, which can be one of the following: 1 i — flip the values of the i-th row; 2 i — flip the values of the i-th column; 3 — output the unusual square of A. Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.OutputLet the number of the 3rd type queries in the input be m. Output a single string s of length m, where the i-th symbol of s is the value of the unusual square of A for the i-th query of the 3rd type as it appears in the input.ExamplesInput31 1 10 1 11 0 01232 332 22 21 3331 22 11 13Output01001	Input31 1 10 1 11 0 01232 332 22 21 3331 22 11 13	Output01001	1 second	256 megabytes	['implementation', 'math', '*1600']
B. Domino Effecttime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Chris knows there's no fun in playing dominoes, he thinks it's too random and doesn't require skill. Instead, he decided to play with the dominoes and make a "domino show".Chris arranges n dominoes in a line, placing each piece vertically upright. In the beginning, he simultaneously pushes some of the dominoes either to the left or to the right. However, somewhere between every two dominoes pushed in the same direction there is at least one domino pushed in the opposite direction.After each second, each domino that is falling to the left pushes the adjacent domino on the left. Similarly, the dominoes falling to the right push their adjacent dominoes standing on the right. When a vertical domino has dominoes falling on it from both sides, it stays still due to the balance of the forces. The figure shows one possible example of the process. Given the initial directions Chris has pushed the dominoes, find the number of the dominoes left standing vertically at the end of the process!InputThe first line contains a single integer n (1 ≤ n ≤ 3000), the number of the dominoes in the line. The next line contains a character string s of length n. The i-th character of the string si is equal to "L", if the i-th domino has been pushed to the left; "R", if the i-th domino has been pushed to the right; ".", if the i-th domino has not been pushed. It is guaranteed that if si = sj = "L" and i < j, then there exists such k that i < k < j and sk = "R"; if si = sj = "R" and i < j, then there exists such k that i < k < j and sk = "L".OutputOutput a single integer, the number of the dominoes that remain vertical at the end of the process.ExamplesInput14.L.R...LR..L..Output4Input5R....Output0Input1.Output1NoteThe first example case is shown on the figure. The four pieces that remain standing vertically are highlighted with orange.In the second example case, all pieces fall down since the first piece topples all the other pieces.In the last example case, a single piece has not been pushed in either direction.	Input14.L.R...LR..L..	Output4	1 second	256 megabytes	['*1100']
A. Gravity Fliptime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLittle Chris is bored during his physics lessons (too easy), so he has built a toy box to keep himself occupied. The box is special, since it has the ability to change gravity.There are n columns of toy cubes in the box arranged in a line. The i-th column contains ai cubes. At first, the gravity in the box is pulling the cubes downwards. When Chris switches the gravity, it begins to pull all the cubes to the right side of the box. The figure shows the initial and final configurations of the cubes in the box: the cubes that have changed their position are highlighted with orange. Given the initial configuration of the toy cubes in the box, find the amounts of cubes in each of the n columns after the gravity switch!InputThe first line of input contains an integer n (1 ≤ n ≤ 100), the number of the columns in the box. The next line contains n space-separated integer numbers. The i-th number ai (1 ≤ ai ≤ 100) denotes the number of cubes in the i-th column.OutputOutput n integer numbers separated by spaces, where the i-th number is the amount of cubes in the i-th column after the gravity switch.ExamplesInput43 2 1 2Output1 2 2 3 Input32 3 8Output2 3 8 NoteThe first example case is shown on the figure. The top cube of the first column falls to the top of the last column; the top cube of the second column falls to the top of the third column; the middle cube of the first column falls to the top of the second column.In the second example case the gravity switch does not change the heights of the columns.	Input43 2 1 2	Output1 2 2 3	1 second	256 megabytes	['greedy', 'implementation', 'sortings', '*900']
E. Maze 1Dtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputValera has a strip infinite in both directions and consisting of cells. The cells are numbered by integers. The cell number 0 has a robot.The robot has instructions — the sequence of moves that he must perform. In one move, the robot moves one cell to the left or one cell to the right, according to instructions. Before the robot starts moving, Valera puts obstacles in some cells of the strip, excluding cell number 0. If the robot should go into the cell with an obstacle according the instructions, it will skip this move.Also Valera indicates the finish cell in which the robot has to be after completing the entire instructions. The finishing cell should be different from the starting one. It is believed that the robot completed the instructions successfully, if during the process of moving he visited the finish cell exactly once — at its last move. Moreover, the latter move cannot be skipped.Let's assume that k is the minimum number of obstacles that Valera must put to make the robot able to complete the entire sequence of instructions successfully and end up in some finishing cell. You need to calculate in how many ways Valera can choose k obstacles and the finishing cell so that the robot is able to complete the instructions successfully.InputThe first line contains a sequence of characters without spaces s1s2... sn (1 ≤ n ≤ 106), consisting only of letters "L" and "R". If character si equals "L", then the robot on the i-th move must try to move one cell to the left. If the si-th character equals "R", then the robot on the i-th move must try to move one cell to the right.OutputPrint a single integer — the required number of ways. It's guaranteed that this number fits into 64-bit signed integer type.ExamplesInputRROutput1InputRRLOutput1NoteIn the first sample Valera mustn't add any obstacles and his finishing cell must be cell 2.In the second sample, Valera must add an obstacle in cell number 1, and his finishing cell must be cell number - 1. In this case robot skips the first two moves and on the third move he goes straight from the starting cell to the finishing one. But if Valera doesn't add any obstacles, or adds an obstacle to another cell, then the robot visits the finishing cell more than once.	InputRR	Output1	1 second	256 megabytes	['binary search', 'greedy', 'implementation', '*2200']
D. Minesweeper 1Dtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputGame "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: 0012*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.InputThe first line contains sequence of characters without spaces s1s2... sn (1 ≤ n ≤ 106), containing only characters "", "?" and digits "0", "1" or "2". If character si equals "", then the i-th cell of the field contains a bomb. If character si equals "?", then Valera hasn't yet decided what to put in the i-th cell. Character si, that is equal to a digit, represents the digit written in the i-th square.OutputPrint 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).ExamplesInput?01???Output4Input?Output2Input12Output0Input1Output0NoteIn the first test sample you can get the following correct fields: 0011, 001**, 0012, 00110.	Input?01???	Output4	2 seconds	512 megabytes	['dp', 'implementation', '*1900']
C. Restore Graphtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputValera had an undirected connected graph without self-loops and multiple edges consisting of n vertices. The graph had an interesting property: there were at most k edges adjacent to each of its vertices. For convenience, we will assume that the graph vertices were indexed by integers from 1 to n.One day Valera counted the shortest distances from one of the graph vertices to all other ones and wrote them out in array d. Thus, element d[i] of the array shows the shortest distance from the vertex Valera chose to vertex number i.Then something irreparable terrible happened. Valera lost the initial graph. However, he still has the array d. Help him restore the lost graph.InputThe first line contains two space-separated integers n and k (1 ≤ k < n ≤ 105). Number n shows the number of vertices in the original graph. Number k shows that at most k edges were adjacent to each vertex in the original graph.The second line contains space-separated integers d[1], d[2], ..., d[n] (0 ≤ d[i] < n). Number d[i] shows the shortest distance from the vertex Valera chose to the vertex number i.OutputIf Valera made a mistake in his notes and the required graph doesn't exist, print in the first line number -1. Otherwise, in the first line print integer m (0 ≤ m ≤ 106) — the number of edges in the found graph.In each of the next m lines print two space-separated integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi), denoting the edge that connects vertices with numbers ai and bi. The graph shouldn't contain self-loops and multiple edges. If there are multiple possible answers, print any of them.ExamplesInput3 20 1 1Output31 21 33 2Input4 22 0 1 3Output31 31 42 3Input3 10 0 0Output-1	Input3 20 1 1	Output31 21 33 2	1 second	256 megabytes	['dfs and similar', 'graphs', 'sortings', '*1800']
B. Marathontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputValera takes part in the Berland Marathon. The marathon race starts at the stadium that can be represented on the plane as a square whose lower left corner is located at point with coordinates (0, 0) and the length of the side equals a meters. The sides of the square are parallel to coordinate axes.As the length of the marathon race is very long, Valera needs to have extra drink during the race. The coach gives Valera a bottle of drink each d meters of the path. We know that Valera starts at the point with coordinates (0, 0) and runs counter-clockwise. That is, when Valera covers a meters, he reaches the point with coordinates (a, 0). We also know that the length of the marathon race equals nd + 0.5 meters. Help Valera's coach determine where he should be located to help Valera. Specifically, determine the coordinates of Valera's positions when he covers d, 2·d, ..., n·d meters.InputThe first line contains two space-separated real numbers a and d (1 ≤ a, d ≤ 105), given with precision till 4 decimal digits after the decimal point. Number a denotes the length of the square's side that describes the stadium. Number d shows that after each d meters Valera gets an extra drink.The second line contains integer n (1 ≤ n ≤ 105) showing that Valera needs an extra drink n times.OutputPrint n lines, each line should contain two real numbers xi and yi, separated by a space. Numbers xi and yi in the i-th line mean that Valera is at point with coordinates (xi, yi) after he covers i·d meters. Your solution will be considered correct if the absolute or relative error doesn't exceed 10 - 4.Note, that this problem have huge amount of output data. Please, do not use cout stream for output in this problem.ExamplesInput2 52Output1.0000000000 2.00000000002.0000000000 0.0000000000Input4.147 2.88196Output2.8819000000 0.00000000004.1470000000 1.61680000003.7953000000 4.14700000000.9134000000 4.14700000000.0000000000 2.17850000000.7034000000 0.0000000000	Input2 52	Output1.0000000000 2.00000000002.0000000000 0.0000000000	1 second	256 megabytes	['implementation', 'math', '*1500']
A. Valera and Xtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputValera is a little boy. Yesterday he got a huge Math hometask at school, so Valera didn't have enough time to properly learn the English alphabet for his English lesson. Unfortunately, the English teacher decided to have a test on alphabet today. At the test Valera got a square piece of squared paper. The length of the side equals n squares (n is an odd number) and each unit square contains some small letter of the English alphabet.Valera needs to know if the letters written on the square piece of paper form letter "X". Valera's teacher thinks that the letters on the piece of paper form an "X", if: on both diagonals of the square paper all letters are the same; all other squares of the paper (they are not on the diagonals) contain the same letter that is different from the letters on the diagonals. Help Valera, write the program that completes the described task for him.InputThe first line contains integer n (3 ≤ n < 300; n is odd). Each of the next n lines contains n small English letters — the description of Valera's paper.OutputPrint string "YES", if the letters on the paper form letter "X". Otherwise, print string "NO". Print the strings without quotes.ExamplesInput5xoooxoxoxosoxoooxoxoxoooxOutputNOInput3wswswswswOutputYESInput3xpxpxpxpeOutputNO	Input5xoooxoxoxosoxoooxoxoxooox	OutputNO	1 second	256 megabytes	['implementation', '*1000']
E. Two Rooted Treestime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou have two rooted undirected trees, each contains n vertices. Let's number the vertices of each tree with integers from 1 to n. The root of each tree is at vertex 1. The edges of the first tree are painted blue, the edges of the second one are painted red. For simplicity, let's say that the first tree is blue and the second tree is red.Edge {x, y} is called bad for edge {p, q} if two conditions are fulfilled: The color of edge {x, y} is different from the color of edge {p, q}. Let's consider the tree of the same color that edge {p, q} is. Exactly one of vertices x, y lies both in the subtree of vertex p and in the subtree of vertex q. In this problem, your task is to simulate the process described below. The process consists of several stages: On each stage edges of exactly one color are deleted. On the first stage, exactly one blue edge is deleted. Let's assume that at the stage i we've deleted edges {u1, v1}, {u2, v2}, ..., {uk, vk}. At the stage i + 1 we will delete all undeleted bad edges for edge {u1, v1}, then we will delete all undeleted bad edges for edge {u2, v2} and so on until we reach edge {uk, vk}. For each stage of deleting edges determine what edges will be removed on the stage. Note that the definition of a bad edge always considers the initial tree before it had any edges removed.InputThe first line contains integer n (2 ≤ n ≤ 2·105) — the number of vertices in each tree.The next line contains n - 1 positive integers a2, a3, ..., an (1 ≤ ai ≤ n; ai ≠ i) — the description of edges of the first tree. Number ai means that the first tree has an edge connecting vertex ai and vertex i.The next line contains n - 1 positive integers b2, b3, ..., bn (1 ≤ bi ≤ n; bi ≠ i) — the description of the edges of the second tree. Number bi means that the second tree has an edge connecting vertex bi and vertex i. The next line contains integer idx (1 ≤ idx < n) — the index of the blue edge that was removed on the first stage. Assume that the edges of each tree are numbered with numbers from 1 to n - 1 in the order in which they are given in the input. OutputFor each stage of removing edges print its description. Each description must consist of exactly two lines. If this is the stage when blue edges are deleted, then the first line of the description must contain word Blue, otherwise — word Red. In the second line print the indexes of the edges that will be deleted on this stage in the increasing order.ExamplesInput51 1 1 14 2 1 13OutputBlue3Red1 3Blue1 2Red2NoteFor simplicity let's assume that all edges of the root tree received some direction, so that all vertices are reachable from vertex 1. Then a subtree of vertex v is a set of vertices reachable from vertex v in the resulting directed graph (vertex v is also included in the set).	Input51 1 1 14 2 1 13	OutputBlue3Red1 3Blue1 2Red2	4 seconds	512 megabytes	['data structures', 'implementation', 'trees', '*2900']
D. Beautiful Pairs of Numberstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe sequence of integer pairs (a1, b1), (a2, b2), ..., (ak, bk) is beautiful, if the following statements are fulfilled: 1 ≤ a1 ≤ b1 < a2 ≤ b2 < ... < ak ≤ bk ≤ n, where n is a given positive integer; all numbers b1 - a1, b2 - a2, ..., bk - ak are distinct. For the given number n find the number of beautiful sequences of length k. As the answer can be rather large, print the remainder after dividing it by 1000000007 (109 + 7).InputThe first line contains integer t (1 ≤ t ≤ 2·105) — the number of the test data.Each of the next t lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000).OutputFor each test from the input print the answer to the problem modulo 1000000007 (109 + 7). Print the answers to the tests in the order in which the tests are given in the input.ExamplesInput61 12 12 23 13 23 3Output130620NoteIn the first test sample there is exactly one beautiful sequence: (1, 1).In the second test sample, the following sequences are beautiful: (1, 1); (1, 2); (2, 2). In the fourth test sample, the following sequences are beautiful: (1, 1); (1, 2); (1, 3); (2, 2); (2, 3); (3, 3). In the fifth test sample, the following sequences are beautiful: (1, 1), (2, 3); (1, 2), (3, 3). In the third and sixth samples, there are no beautiful sequences.	Input61 12 12 23 13 23 3	Output130620	3 seconds	256 megabytes	['combinatorics', 'dp', '*2300']
E. Strictly Positive Matrixtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou have matrix a of size n × n. Let's number the rows of the matrix from 1 to n from top to bottom, let's number the columns from 1 to n from left to right. Let's use aij to represent the element on the intersection of the i-th row and the j-th column. Matrix a meets the following two conditions: for any numbers i, j (1 ≤ i, j ≤ n) the following inequality holds: aij ≥ 0; . Matrix b is strictly positive, if for any numbers i, j (1 ≤ i, j ≤ n) the inequality bij > 0 holds. You task is to determine if there is such integer k ≥ 1, that matrix ak is strictly positive.InputThe first line contains integer n (2 ≤ n ≤ 2000) — the number of rows and columns in matrix a.The next n lines contain the description of the rows of matrix a. The i-th line contains n non-negative integers ai1, ai2, ..., ain (0 ≤ aij ≤ 50). It is guaranteed that .OutputIf there is a positive integer k ≥ 1, such that matrix ak is strictly positive, print "YES" (without the quotes). Otherwise, print "NO" (without the quotes). ExamplesInput21 00 1OutputNOInput54 5 6 1 21 2 3 4 56 4 1 2 41 1 1 1 14 4 4 4 4OutputYES	Input21 00 1	OutputNO	1 second	256 megabytes	['graphs', 'math', '*2200']
D. Upgrading Arraytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou have an array of positive integers a[1], a[2], ..., a[n] and a set of bad prime numbers b1, b2, ..., bm. The prime numbers that do not occur in the set b are considered good. The beauty of array a is the sum , where function f(s) is determined as follows: f(1) = 0; Let's assume that p is the minimum prime divisor of s. If p is a good prime, then , otherwise . You are allowed to perform an arbitrary (probably zero) number of operations to improve array a. The operation of improvement is the following sequence of actions: Choose some number r (1 ≤ r ≤ n) and calculate the value g = GCD(a[1], a[2], ..., a[r]). Apply the assignments: , , ..., . What is the maximum beauty of the array you can get? InputThe first line contains two integers n and m (1 ≤ n, m ≤ 5000) showing how many numbers are in the array and how many bad prime numbers there are.The second line contains n space-separated integers a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ 109) — array a. The third line contains m space-separated integers b1, b2, ..., bm (2 ≤ b1 < b2 < ... < bm ≤ 109) — the set of bad prime numbers.OutputPrint a single integer — the answer to the problem.ExamplesInput5 24 20 34 10 102 5Output-2Input4 52 4 8 163 5 7 11 17Output10NoteNote that the answer to the problem can be negative.The GCD(x1, x2, ..., xk) is the maximum positive integer that divides each xi.	Input5 24 20 34 10 102 5	Output-2	1 second	256 megabytes	['dp', 'greedy', 'math', 'number theory', '*1800']
C. Searching for Graphtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet's call an undirected graph of n vertices p-interesting, if the following conditions fulfill: the graph contains exactly 2n + p edges; the graph doesn't contain self-loops and multiple edges; for any integer k (1 ≤ k ≤ n), any subgraph consisting of k vertices contains at most 2k + p edges. A subgraph of a graph is some set of the graph vertices and some set of the graph edges. At that, the set of edges must meet the condition: both ends of each edge from the set must belong to the chosen set of vertices. Your task is to find a p-interesting graph consisting of n vertices.InputThe first line contains a single integer t (1 ≤ t ≤ 5) — the number of tests in the input. Next t lines each contains two space-separated integers: n, p (5 ≤ n ≤ 24; p ≥ 0; ) — the number of vertices in the graph and the interest value for the appropriate test. It is guaranteed that the required graph exists.OutputFor each of the t tests print 2n + p lines containing the description of the edges of a p-interesting graph: the i-th line must contain two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — two vertices, connected by an edge in the resulting graph. Consider the graph vertices numbered with integers from 1 to n. Print the answers to the tests in the order the tests occur in the input. If there are multiple solutions, you can print any of them.ExamplesInput16 0Output1 21 31 41 51 62 32 42 52 63 43 53 6	Input16 0	Output1 21 31 41 51 62 32 42 52 63 43 53 6	1 second	256 megabytes	['brute force', 'constructive algorithms', 'graphs', '*1500']
B. Trees in a Rowtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe Queen of England has n trees growing in a row in her garden. At that, the i-th (1 ≤ i ≤ n) tree from the left has height ai meters. Today the Queen decided to update the scenery of her garden. She wants the trees' heights to meet the condition: for all i (1 ≤ i < n), ai + 1 - ai = k, where k is the number the Queen chose.Unfortunately, the royal gardener is not a machine and he cannot fulfill the desire of the Queen instantly! In one minute, the gardener can either decrease the height of a tree to any positive integer height or increase the height of a tree to any positive integer height. How should the royal gardener act to fulfill a whim of Her Majesty in the minimum number of minutes?InputThe first line contains two space-separated integers: n, k (1 ≤ n, k ≤ 1000). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the heights of the trees in the row. OutputIn the first line print a single integer p — the minimum number of minutes the gardener needs. In the next p lines print the description of his actions. If the gardener needs to increase the height of the j-th (1 ≤ j ≤ n) tree from the left by x (x ≥ 1) meters, then print in the corresponding line "+ j x". If the gardener needs to decrease the height of the j-th (1 ≤ j ≤ n) tree from the left by x (x ≥ 1) meters, print on the corresponding line "- j x".If there are multiple ways to make a row of trees beautiful in the minimum number of actions, you are allowed to print any of them.ExamplesInput4 11 2 1 5Output2+ 3 2- 4 1Input4 11 2 3 4Output0	Input4 11 2 1 5	Output2+ 3 2- 4 1	1 second	256 megabytes	['brute force', 'implementation', '*1400']
A. Nutstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou have a nuts and lots of boxes. The boxes have a wonderful feature: if you put x (x ≥ 0) divisors (the spacial bars that can divide a box) to it, you get a box, divided into x + 1 sections.You are minimalist. Therefore, on the one hand, you are against dividing some box into more than k sections. On the other hand, you are against putting more than v nuts into some section of the box. What is the minimum number of boxes you have to use if you want to put all the nuts in boxes, and you have b divisors?Please note that you need to minimize the number of used boxes, not sections. You do not have to minimize the number of used divisors.InputThe first line contains four space-separated integers k, a, b, v (2 ≤ k ≤ 1000; 1 ≤ a, b, v ≤ 1000) — the maximum number of sections in the box, the number of nuts, the number of divisors and the capacity of each section of the box.OutputPrint a single integer — the answer to the problem.ExamplesInput3 10 3 3Output2Input3 10 1 3Output3Input100 100 1 1000Output1NoteIn the first sample you can act like this: Put two divisors to the first box. Now the first box has three sections and we can put three nuts into each section. Overall, the first box will have nine nuts. Do not put any divisors into the second box. Thus, the second box has one section for the last nut. In the end we've put all the ten nuts into boxes.The second sample is different as we have exactly one divisor and we put it to the first box. The next two boxes will have one section each.	Input3 10 3 3	Output2	1 second	256 megabytes	['greedy', 'math', '*1100']

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