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Instructors of Some Informatics School make students go to bed.The house contains n rooms, in each room exactly b students were supposed to sleep. However, at the time of curfew it happened that many students are not located in their assigned rooms. The rooms are arranged in a row and numbered from 1 to n. Initially, in i-th room there are ai students. All students are currently somewhere in the house, therefore a1 + a2 + ... + an = nb. Also 2 instructors live in this house.The process of curfew enforcement is the following. One instructor starts near room 1 and moves toward room n, while the second instructor starts near room n and moves toward room 1. After processing current room, each instructor moves on to the next one. Both instructors enter rooms and move simultaneously, if n is odd, then only the first instructor processes the middle room. When all rooms are processed, the process ends.When an instructor processes a room, she counts the number of students in the room, then turns off the light, and locks the room. Also, if the number of students inside the processed room is not equal to b, the instructor writes down the number of this room into her notebook (and turns off the light, and locks the room). Instructors are in a hurry (to prepare the study plan for the next day), so they don't care about who is in the room, but only about the number of students.While instructors are inside the rooms, students can run between rooms that are not locked and not being processed. A student can run by at most d rooms, that is she can move to a room with number that differs my at most d. Also, after (or instead of) running each student can hide under a bed in a room she is in. In this case the instructor will not count her during the processing. In each room any number of students can hide simultaneously.Formally, here is what's happening: A curfew is announced, at this point in room i there are ai students. Each student can run to another room but not further than d rooms away from her initial room, or stay in place. After that each student can optionally hide under a bed. Instructors enter room 1 and room n, they count students there and lock the room (after it no one can enter or leave this room). Each student from rooms with numbers from 2 to n - 1 can run to another room but not further than d rooms away from her current room, or stay in place. Each student can optionally hide under a bed. Instructors move from room 1 to room 2 and from room n to room n - 1. This process continues until all rooms are processed. Let x1 denote the number of rooms in which the first instructor counted the number of non-hidden students different from b, and x2 be the same number for the second instructor. Students know that the principal will only listen to one complaint, therefore they want to minimize the maximum of numbers xi. Help them find this value if they use the optimal strategy. | Input: ['5 1 11 0 0 0 4'] Output:['1'] | [
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Dima is a beginner programmer. During his working process, he regularly has to repeat the following operation again and again: to remove every second element from the array. One day he has been bored with easy solutions of this problem, and he has come up with the following extravagant algorithm.Let's consider that initially array contains n numbers from 1 to n and the number i is located in the cell with the index 2i - 1 (Indices are numbered starting from one) and other cells of the array are empty. Each step Dima selects a non-empty array cell with the maximum index and moves the number written in it to the nearest empty cell to the left of the selected one. The process continues until all n numbers will appear in the first n cells of the array. For example if n = 4, the array is changing as follows: You have to write a program that allows you to determine what number will be in the cell with index x (1 ≤ x ≤ n) after Dima's algorithm finishes. | Input: ['4 3234'] Output:['324'] | [
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Oleg writes down the history of the days he lived. For each day he decides if it was good or bad. Oleg calls a non-empty sequence of days a zebra, if it starts with a bad day, ends with a bad day, and good and bad days are alternating in it. Let us denote bad days as 0 and good days as 1. Then, for example, sequences of days 0, 010, 01010 are zebras, while sequences 1, 0110, 0101 are not.Oleg tells you the story of days he lived in chronological order in form of string consisting of 0 and 1. Now you are interested if it is possible to divide Oleg's life history into several subsequences, each of which is a zebra, and the way it can be done. Each day must belong to exactly one of the subsequences. For each of the subsequences, days forming it must be ordered chronologically. Note that subsequence does not have to be a group of consecutive days. | Input: ['0010100'] Output:['33 1 3 43 2 5 61 7'] | [
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Bob is a farmer. He has a large pasture with many sheep. Recently, he has lost some of them due to wolf attacks. He thus decided to place some shepherd dogs in such a way that all his sheep are protected.The pasture is a rectangle consisting of R × C cells. Each cell is either empty, contains a sheep, a wolf or a dog. Sheep and dogs always stay in place, but wolves can roam freely around the pasture, by repeatedly moving to the left, right, up or down to a neighboring cell. When a wolf enters a cell with a sheep, it consumes it. However, no wolf can enter a cell with a dog.Initially there are no dogs. Place dogs onto the pasture in such a way that no wolf can reach any sheep, or determine that it is impossible. Note that since you have many dogs, you do not need to minimize their number. | Input: ['6 6..S.....S.W..S......W......W........'] Output:['Yes..SD....SDW..SD....DW...DD.W........'] | [
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Yes, that's another problem with definition of "beautiful" numbers.Let's call a positive integer x beautiful if its decimal representation without leading zeroes contains even number of digits, and there exists a permutation of this representation which is palindromic. For example, 4242 is a beautiful number, since it contains 4 digits, and there exists a palindromic permutation 2442.Given a positive integer s, find the largest beautiful number which is less than s. | Input: ['48988100028923845'] Output:['88779928923839'] | [
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You are given a string s consisting of |s| small english letters.In one move you can replace any character of this string to the next character in alphabetical order (a will be replaced with b, s will be replaced with t, etc.). You cannot replace letter z with any other letter.Your target is to make some number of moves (not necessary minimal) to get string abcdefghijklmnopqrstuvwxyz (english alphabet) as a subsequence. Subsequence of the string is the string that is obtained by deleting characters at some positions. You need to print the string that will be obtained from the given string and will be contain english alphabet as a subsequence or say that it is impossible. | Input: ['aacceeggiikkmmooqqssuuwwyy'] Output:['abcdefghijklmnopqrstuvwxyz'] | [
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You have two variables a and b. Consider the following sequence of actions performed with these variables: If a = 0 or b = 0, end the process. Otherwise, go to step 2; If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3; If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.Initially the values of a and b are positive integers, and so the process will be finite.You have to determine the values of a and b after the process ends. | Input: ['12 5'] Output:['0 1'] | [
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You are given a sequence a consisting of n integers. You may partition this sequence into two sequences b and c in such a way that every element belongs exactly to one of these sequences. Let B be the sum of elements belonging to b, and C be the sum of elements belonging to c (if some of these sequences is empty, then its sum is 0). What is the maximum possible value of B - C? | Input: ['31 -2 0'] Output:['3'] | [
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You come home and fell some unpleasant smell. Where is it coming from?You are given an array a. You have to answer the following queries: You are given two integers l and r. Let ci be the number of occurrences of i in al: r, where al: r is the subarray of a from l-th element to r-th inclusive. Find the Mex of {c0, c1, ..., c109} You are given two integers p to x. Change ap to x. The Mex of a multiset of numbers is the smallest non-negative integer not in the set.Note that in this problem all elements of a are positive, which means that c0 = 0 and 0 is never the answer for the query of the second type. | Input: ['10 41 2 3 1 1 2 2 2 9 91 1 11 2 82 7 11 2 8'] Output:['232'] | [
0
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Since you are the best Wraith King, Nizhniy Magazin «Mir» at the centre of Vinnytsia is offering you a discount.You are given an array a of length n and an integer c. The value of some array b of length k is the sum of its elements except for the smallest. For example, the value of the array [3, 1, 6, 5, 2] with c = 2 is 3 + 6 + 5 = 14.Among all possible partitions of a into contiguous subarrays output the smallest possible sum of the values of these subarrays. | Input: ['3 51 2 3'] Output:['6'] | [
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"We've tried solitary confinement, waterboarding and listening to Just In Beaver, to no avail. We need something extreme.""Little Alena got an array as a birthday present..."The array b of length n is obtained from the array a of length n and two integers l and r (l ≤ r) using the following procedure:b1 = b2 = b3 = b4 = 0.For all 5 ≤ i ≤ n: bi = 0 if ai, ai - 1, ai - 2, ai - 3, ai - 4 > r and bi - 1 = bi - 2 = bi - 3 = bi - 4 = 1 bi = 1 if ai, ai - 1, ai - 2, ai - 3, ai - 4 < l and bi - 1 = bi - 2 = bi - 3 = bi - 4 = 0 bi = bi - 1 otherwise You are given arrays a and b' of the same length. Find two integers l and r (l ≤ r), such that applying the algorithm described above will yield an array b equal to b'.It's guaranteed that the answer exists. | Input: ['51 2 3 4 500001'] Output:['6 15'] | [
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Right now she actually isn't. But she will be, if you don't solve this problem.You are given integers n, k, A and B. There is a number x, which is initially equal to n. You are allowed to perform two types of operations: Subtract 1 from x. This operation costs you A coins. Divide x by k. Can be performed only if x is divisible by k. This operation costs you B coins. What is the minimum amount of coins you have to pay to make x equal to 1? | Input: ['9231'] Output:['6'] | [
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We've got no test cases. A big olympiad is coming up. But the problemsetters' number one priority should be adding another problem to the round. The diameter of a multiset of points on the line is the largest distance between two points from this set. For example, the diameter of the multiset {1, 3, 2, 1} is 2.Diameter of multiset consisting of one point is 0.You are given n points on the line. What is the minimum number of points you have to remove, so that the diameter of the multiset of the remaining points will not exceed d? | Input: ['3 12 1 4'] Output:['1'] | [
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You are given a multiset S consisting of positive integers (initially empty). There are two kind of queries: Add a positive integer to S, the newly added integer is not less than any number in it. Find a subset s of the set S such that the value is maximum possible. Here max(s) means maximum value of elements in s, — the average value of numbers in s. Output this maximum possible value of . | Input: ['61 321 421 82'] Output:['0.00000000000.50000000003.0000000000'] | [
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] |
Valya and Tolya are an ideal pair, but they quarrel sometimes. Recently, Valya took offense at her boyfriend because he came to her in t-shirt with lettering that differs from lettering on her pullover. Now she doesn't want to see him and Tolya is seating at his room and crying at her photos all day long.This story could be very sad but fairy godmother (Tolya's grandmother) decided to help them and restore their relationship. She secretly took Tolya's t-shirt and Valya's pullover and wants to make the letterings on them same. In order to do this, for one unit of mana she can buy a spell that can change some letters on the clothes. Your task is calculate the minimum amount of mana that Tolya's grandmother should spend to rescue love of Tolya and Valya.More formally, letterings on Tolya's t-shirt and Valya's pullover are two strings with same length n consisting only of lowercase English letters. Using one unit of mana, grandmother can buy a spell of form (c1, c2) (where c1 and c2 are some lowercase English letters), which can arbitrary number of times transform a single letter c1 to c2 and vise-versa on both Tolya's t-shirt and Valya's pullover. You should find the minimum amount of mana that grandmother should spend to buy a set of spells that can make the letterings equal. In addition you should output the required set of spells. | Input: ['3abbdad'] Output:['2a db a'] | [
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In distant future on Earth day lasts for n hours and that's why there are n timezones. Local times in adjacent timezones differ by one hour. For describing local time, hours numbers from 1 to n are used, i.e. there is no time "0 hours", instead of it "n hours" is used. When local time in the 1-st timezone is 1 hour, local time in the i-th timezone is i hours.Some online programming contests platform wants to conduct a contest that lasts for an hour in such a way that its beginning coincides with beginning of some hour (in all time zones). The platform knows, that there are ai people from i-th timezone who want to participate in the contest. Each person will participate if and only if the contest starts no earlier than s hours 00 minutes local time and ends not later than f hours 00 minutes local time. Values s and f are equal for all time zones. If the contest starts at f hours 00 minutes local time, the person won't participate in it.Help platform select such an hour, that the number of people who will participate in the contest is maximum. | Input: ['31 2 31 3'] Output:['3'] | [
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You are given a string s, initially consisting of n lowercase Latin letters. After that, you perform k operations with it, where . During i-th operation you must erase some substring of length exactly 2i - 1 from s.Print the lexicographically minimal string you may obtain after performing k such operations. | Input: ['adcbca'] Output:['aba'] | [
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You are given an array a of length n. We define fa the following way: Initially fa = 0, M = 1; for every 2 ≤ i ≤ n if aM < ai then we set fa = fa + aM and then set M = i. Calculate the sum of fa over all n! permutations of the array a modulo 109 + 7.Note: two elements are considered different if their indices differ, so for every array a there are exactly n! permutations. | Input: ['21 3'] Output:['1'] | [
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Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero. Consider the following problem:You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.You don't have to solve this problem. Instead, you have to construct a few tests for it.You will be given t numbers x1, x2, ..., xt. For every , find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi. | Input: ['32101'] Output:['5 21 1-1'] | [
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You and your friend are participating in a TV show "Run For Your Prize".At the start of the show n prizes are located on a straight line. i-th prize is located at position ai. Positions of all prizes are distinct. You start at position 1, your friend — at position 106 (and there is no prize in any of these two positions). You have to work as a team and collect all prizes in minimum possible time, in any order.You know that it takes exactly 1 second to move from position x to position x + 1 or x - 1, both for you and your friend. You also have trained enough to instantly pick up any prize, if its position is equal to your current position (and the same is true for your friend). Carrying prizes does not affect your speed (or your friend's speed) at all.Now you may discuss your strategy with your friend and decide who will pick up each prize. Remember that every prize must be picked up, either by you or by your friend.What is the minimum number of seconds it will take to pick up all the prizes? | Input: ['32 3 9'] Output:['8'] | [
0,
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] |
The weather is fine today and hence it's high time to climb the nearby pine and enjoy the landscape.The pine's trunk includes several branches, located one above another and numbered from 2 to y. Some of them (more precise, from 2 to p) are occupied by tiny vile grasshoppers which you're at war with. These grasshoppers are known for their awesome jumping skills: the grasshopper at branch x can jump to branches .Keeping this in mind, you wisely decided to choose such a branch that none of the grasshoppers could interrupt you. At the same time you wanna settle as high as possible since the view from up there is simply breathtaking.In other words, your goal is to find the highest branch that cannot be reached by any of the grasshoppers or report that it's impossible. | Input: ['3 6'] Output:['5'] | [
0,
3
] |
Vitya loves programming and problem solving, but sometimes, to distract himself a little, he plays computer games. Once he found a new interesting game about tanks, and he liked it so much that he went through almost all levels in one day. Remained only the last level, which was too tricky. Then Vitya remembered that he is a programmer, and wrote a program that helped him to pass this difficult level. Try do the same.The game is organized as follows. There is a long road, two cells wide and n cells long. Some cells have obstacles. You control a tank that occupies one cell. Initially, the tank is located before the start of the road, in a cell with coordinates (0, 1). Your task is to move the tank to the end of the road, to the cell (n + 1, 1) or (n + 1, 2). Every second the tank moves one cell to the right: the coordinate x is increased by one. When you press the up or down arrow keys, the tank instantly changes the lane, that is, the y coordinate. When you press the spacebar, the tank shoots, and the nearest obstacle along the lane in which the tank rides is instantly destroyed. In order to load a gun, the tank needs t seconds. Initially, the gun is not loaded, that means, the first shot can be made only after t seconds after the tank starts to move.If at some point the tank is in the same cell with an obstacle not yet destroyed, it burns out. If you press the arrow exactly at the moment when the tank moves forward, the tank will first move forward, and then change the lane, so it will not be possible to move diagonally.Your task is to find out whether it is possible to pass the level, and if possible, to find the order of actions the player need to make. | Input: ['6 2 3 22 63 5 6'] Output:['Yes20 3 22 24 1'] | [
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Julia is going to cook a chicken in the kitchen of her dormitory. To save energy, the stove in the kitchen automatically turns off after k minutes after turning on.During cooking, Julia goes to the kitchen every d minutes and turns on the stove if it is turned off. While the cooker is turned off, it stays warm. The stove switches on and off instantly.It is known that the chicken needs t minutes to be cooked on the stove, if it is turned on, and 2t minutes, if it is turned off. You need to find out, how much time will Julia have to cook the chicken, if it is considered that the chicken is cooked evenly, with constant speed when the stove is turned on and at a constant speed when it is turned off. | Input: ['3 2 6'] Output:['6.5'] | [
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Fafa has an array A of n positive integers, the function f(A) is defined as . He wants to do q queries of two types: 1 l r x — find the maximum possible value of f(A), if x is to be added to one element in the range [l, r]. You can choose to which element to add x. 2 l r x — increase all the elements in the range [l, r] by value x. Note that queries of type 1 don't affect the array elements. | Input: ['51 1 1 1 151 2 4 12 2 3 12 4 4 22 3 4 11 3 3 2'] Output:['28'] | [
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Ancient Egyptians are known to have used a large set of symbols to write on the walls of the temples. Fafa and Fifa went to one of the temples and found two non-empty words S1 and S2 of equal lengths on the wall of temple written one below the other. Since this temple is very ancient, some symbols from the words were erased. The symbols in the set have equal probability for being in the position of any erased symbol.Fifa challenged Fafa to calculate the probability that S1 is lexicographically greater than S2. Can you help Fafa with this task?You know that , i. e. there were m distinct characters in Egyptians' alphabet, in this problem these characters are denoted by integers from 1 to m in alphabet order. A word x is lexicographically greater than a word y of the same length, if the words are same up to some position, and then the word x has a larger character, than the word y.We can prove that the probability equals to some fraction , where P and Q are coprime integers, and . Print as the answer the value , i. e. such a non-negative integer less than 109 + 7, such that , where means that a and b give the same remainders when divided by m. | Input: ['1 201'] Output:['500000004'] | [
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Fafa owns a company that works on huge projects. There are n employees in Fafa's company. Whenever the company has a new project to start working on, Fafa has to divide the tasks of this project among all the employees.Fafa finds doing this every time is very tiring for him. So, he decided to choose the best l employees in his company as team leaders. Whenever there is a new project, Fafa will divide the tasks among only the team leaders and each team leader will be responsible of some positive number of employees to give them the tasks. To make this process fair for the team leaders, each one of them should be responsible for the same number of employees. Moreover, every employee, who is not a team leader, has to be under the responsibility of exactly one team leader, and no team leader is responsible for another team leader.Given the number of employees n, find in how many ways Fafa could choose the number of team leaders l in such a way that it is possible to divide employees between them evenly. | Input: ['2'] Output:['1'] | [
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Nian is a monster which lives deep in the oceans. Once a year, it shows up on the land, devouring livestock and even people. In order to keep the monster away, people fill their villages with red colour, light, and cracking noise, all of which frighten the monster out of coming.Little Tommy has n lanterns and Big Banban has m lanterns. Tommy's lanterns have brightness a1, a2, ..., an, and Banban's have brightness b1, b2, ..., bm respectively.Tommy intends to hide one of his lanterns, then Banban picks one of Tommy's non-hidden lanterns and one of his own lanterns to form a pair. The pair's brightness will be the product of the brightness of two lanterns.Tommy wants to make the product as small as possible, while Banban tries to make it as large as possible.You are asked to find the brightness of the chosen pair if both of them choose optimally. | Input: ['2 220 182 14'] Output:['252'] | [
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Everything red frightens Nian the monster. So do red paper and... you, red on Codeforces, potential or real.Big Banban has got a piece of paper with endless lattice points, where lattice points form squares with the same area. His most favorite closed shape is the circle because of its beauty and simplicity. Once he had obtained this piece of paper, he prepares it for paper-cutting. He drew n concentric circles on it and numbered these circles from 1 to n such that the center of each circle is the same lattice point and the radius of the k-th circle is times the length of a lattice edge.Define the degree of beauty of a lattice point as the summation of the indices of circles such that this lattice point is inside them, or on their bounds. Banban wanted to ask you the total degree of beauty of all the lattice points, but changed his mind.Defining the total degree of beauty of all the lattice points on a piece of paper with n circles as f(n), you are asked to figure out . | Input: ['5'] Output:['387'] | [
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In order to put away old things and welcome a fresh new year, a thorough cleaning of the house is a must.Little Tommy finds an old polynomial and cleaned it up by taking it modulo another. But now he regrets doing this...Given two integers p and k, find a polynomial f(x) with non-negative integer coefficients strictly less than k, whose remainder is p when divided by (x + k). That is, f(x) = q(x)·(x + k) + p, where q(x) is a polynomial (not necessarily with integer coefficients). | Input: ['46 2'] Output:['70 1 0 0 1 1 1'] | [
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You have a team of N people. For a particular task, you can pick any non-empty subset of people. The cost of having x people for the task is xk. Output the sum of costs over all non-empty subsets of people. | Input: ['1 1'] Output:['1'] | [
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You are given a node of the tree with index 1 and with weight 0. Let cnt be the number of nodes in the tree at any instant (initially, cnt is set to 1). Support Q queries of following two types: Add a new node (index cnt + 1) with weight W and add edge between node R and this node. Output the maximum length of sequence of nodes which starts with R. Every node in the sequence is an ancestor of its predecessor. Sum of weight of nodes in sequence does not exceed X. For some nodes i, j that are consecutive in the sequence if i is an ancestor of j then w[i] ≥ w[j] and there should not exist a node k on simple path from i to j such that w[k] ≥ w[j] The tree is rooted at node 1 at any instant.Note that the queries are given in a modified way. | Input: ['61 1 12 2 02 2 11 3 02 2 02 2 2'] Output:['0112'] | [
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For a permutation P[1... N] of integers from 1 to N, function f is defined as follows: Let g(i) be the minimum positive integer j such that f(i, j) = i. We can show such j always exists.For given N, A, B, find a permutation P of integers from 1 to N such that for 1 ≤ i ≤ N, g(i) equals either A or B. | Input: ['9 2 5'] Output:['6 5 8 3 4 1 9 2 7'] | [
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Let us define two functions f and g on positive integer numbers. You need to process Q queries. In each query, you will be given three integers l, r and k. You need to print the number of integers x between l and r inclusive, such that g(x) = k. | Input: ['422 73 945 64 647 55 72 62 4'] Output:['1408'] | [
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Anya and Kirill are doing a physics laboratory work. In one of the tasks they have to measure some value n times, and then compute the average value to lower the error.Kirill has already made his measurements, and has got the following integer values: x1, x2, ..., xn. It is important that the values are close to each other, namely, the difference between the maximum value and the minimum value is at most 2.Anya does not want to make the measurements, however, she can't just copy the values from Kirill's work, because the error of each measurement is a random value, and this coincidence will be noted by the teacher. Anya wants to write such integer values y1, y2, ..., yn in her work, that the following conditions are met: the average value of x1, x2, ..., xn is equal to the average value of y1, y2, ..., yn; all Anya's measurements are in the same bounds as all Kirill's measurements, that is, the maximum value among Anya's values is not greater than the maximum value among Kirill's values, and the minimum value among Anya's values is not less than the minimum value among Kirill's values; the number of equal measurements in Anya's work and Kirill's work is as small as possible among options with the previous conditions met. Formally, the teacher goes through all Anya's values one by one, if there is equal value in Kirill's work and it is not strike off yet, he strikes off this Anya's value and one of equal values in Kirill's work. The number of equal measurements is then the total number of strike off values in Anya's work. Help Anya to write such a set of measurements that the conditions above are met. | Input: ['6-1 1 1 0 0 -1'] Output:['20 0 0 0 0 0 '] | [
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Two friends are on the coordinate axis Ox in points with integer coordinates. One of them is in the point x1 = a, another one is in the point x2 = b. Each of the friends can move by one along the line in any direction unlimited number of times. When a friend moves, the tiredness of a friend changes according to the following rules: the first move increases the tiredness by 1, the second move increases the tiredness by 2, the third — by 3 and so on. For example, if a friend moves first to the left, then to the right (returning to the same point), and then again to the left his tiredness becomes equal to 1 + 2 + 3 = 6.The friends want to meet in a integer point. Determine the minimum total tiredness they should gain, if they meet in the same point. | Input: ['34'] Output:['1'] | [
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Arkady and Kirill visited an exhibition of rare coins. The coins were located in a row and enumerated from left to right from 1 to k, each coin either was laid with its obverse (front) side up, or with its reverse (back) side up.Arkady and Kirill made some photos of the coins, each photo contained a segment of neighboring coins. Akrady is interested in obverses, so on each photo made by him there is at least one coin with obverse side up. On the contrary, Kirill is interested in reverses, so on each photo made by him there is at least one coin with its reverse side up.The photos are lost now, but Arkady and Kirill still remember the bounds of the segments of coins each photo contained. Given this information, compute the remainder of division by 109 + 7 of the number of ways to choose the upper side of each coin in such a way, that on each Arkady's photo there is at least one coin with obverse side up, and on each Kirill's photo there is at least one coin with reverse side up. | Input: ['5 2 21 33 52 24 5'] Output:['8'] | [
3
] |
Завтра у хоккейной команды, которой руководит Евгений, важный матч. Евгению нужно выбрать шесть игроков, которые выйдут на лед в стартовом составе: один вратарь, два защитника и три нападающих.Так как это стартовый состав, Евгения больше волнует, насколько красива будет команда на льду, чем способности игроков. А именно, Евгений хочет выбрать такой стартовый состав, чтобы номера любых двух игроков из стартового состава отличались не более, чем в два раза. Например, игроки с номерами 13, 14, 10, 18, 15 и 20 устроят Евгения, а если, например, на лед выйдут игроки с номерами 8 и 17, то это не устроит Евгения.Про каждого из игроков вам известно, на какой позиции он играет (вратарь, защитник или нападающий), а также его номер. В хоккее номера игроков не обязательно идут подряд. Посчитайте число различных стартовых составов из одного вратаря, двух защитников и трех нападающих, которые может выбрать Евгений, чтобы выполнялось его условие красоты. | Input: ['1 2 31510 1920 11 13'] Output:['1'] | [
3
] |
Как известно, в теплую погоду многие жители крупных городов пользуются сервисами городского велопроката. Вот и Аркадий сегодня будет добираться от школы до дома, используя городские велосипеды.Школа и дом находятся на одной прямой улице, кроме того, на той же улице есть n точек, где можно взять велосипед в прокат или сдать его. Первый велопрокат находится в точке x1 километров вдоль улицы, второй — в точке x2 и так далее, n-й велопрокат находится в точке xn. Школа Аркадия находится в точке x1 (то есть там же, где и первый велопрокат), а дом — в точке xn (то есть там же, где и n-й велопрокат). Известно, что xi < xi + 1 для всех 1 ≤ i < n.Согласно правилам пользования велопроката, Аркадий может брать велосипед в прокат только на ограниченное время, после этого он должен обязательно вернуть его в одной из точек велопроката, однако, он тут же может взять новый велосипед, и отсчет времени пойдет заново. Аркадий может брать не более одного велосипеда в прокат одновременно. Если Аркадий решает взять велосипед в какой-то точке проката, то он сдаёт тот велосипед, на котором он до него доехал, берёт ровно один новый велосипед и продолжает на нём своё движение.За отведенное время, независимо от выбранного велосипеда, Аркадий успевает проехать не больше k километров вдоль улицы. Определите, сможет ли Аркадий доехать на велосипедах от школы до дома, и если да, то какое минимальное число раз ему необходимо будет взять велосипед в прокат, включая первый велосипед? Учтите, что Аркадий не намерен сегодня ходить пешком. | Input: ['4 43 6 8 10'] Output:['2'] | [
2
] |
A positive integer is called a 2-3-integer, if it is equal to 2x·3y for some non-negative integers x and y. In other words, these integers are such integers that only have 2 and 3 among their prime divisors. For example, integers 1, 6, 9, 16 and 108 — are 2-3 integers, while 5, 10, 21 and 120 are not.Print the number of 2-3-integers on the given segment [l, r], i. e. the number of sich 2-3-integers t that l ≤ t ≤ r. | Input: ['1 10'] Output:['7'] | [
3
] |
Vova has recently learned what a circulaton in a graph is. Recall the definition: let G = (V, E) be a directed graph. A circulation f is such a collection of non-negative real numbers f_e (e \in E), that for each vertex v \in V the following conservation condition holds:\sum\limits_{e \in \delta^{-}(v)} f_e = \sum\limits_{e \in \delta^{+}(v)} f_ewhere \delta^{+}(v) is the set of edges that end in the vertex v, and \delta^{-}(v) is the set of edges that start in the vertex v. In other words, for each vertex the total incoming flow should be equal to the total outcoming flow.Let a lr-circulation be such a circulation f that for each edge the condition l_e <=q f_e <=q r_e holds, where l_e and r_e for each edge e \in E are two non-negative real numbers denoting the lower and upper bounds on the value of the circulation on this edge e.Vova can't stop thinking about applications of a new topic. Right now he thinks about the following natural question: let the graph be fixed, and each value l_e and r_e be a linear function of a real variable t:l_e(t) = a_e t + b_e r_e(t) = c_e t + d_eNote that t is the same for all edges.Let t be chosen at random from uniform distribution on a segment [0, 1]. What is the probability of existence of lr-circulation in the graph? | Input: ['3 31 2 0 3 -4 72 3 -2 5 1 63 1 0 4 0 4'] Output:['0.25'] | [
4
] |
Vitya has learned that the answer for The Ultimate Question of Life, the Universe, and Everything is not the integer 54 42, but an increasing integer sequence a_1, ..., a_n. In order to not reveal the secret earlier than needed, Vitya encrypted the answer and obtained the sequence b_1, ..., b_n using the following rules: b_1 = a_1; b_i = a_i \oplus a_{i - 1} for all i from 2 to n, where x \oplus y is the bitwise XOR of x and y. It is easy to see that the original sequence can be obtained using the rule a_i = b_1 \oplus ... \oplus b_i.However, some time later Vitya discovered that the integers b_i in the cypher got shuffled, and it can happen that when decrypted using the rule mentioned above, it can produce a sequence that is not increasing. In order to save his reputation in the scientific community, Vasya decided to find some permutation of integers b_i so that the sequence a_i = b_1 \oplus ... \oplus b_i is strictly increasing. Help him find such a permutation or determine that it is impossible. | Input: ['31 2 3'] Output:['No'] | [
3
] |
One department of some software company has n servers of different specifications. Servers are indexed with consecutive integers from 1 to n. Suppose that the specifications of the j-th server may be expressed with a single integer number c_j of artificial resource units.In order for production to work, it is needed to deploy two services S_1 and S_2 to process incoming requests using the servers of the department. Processing of incoming requests of service S_i takes x_i resource units.The described situation happens in an advanced company, that is why each service may be deployed using not only one server, but several servers simultaneously. If service S_i is deployed using k_i servers, then the load is divided equally between these servers and each server requires only x_i / k_i (that may be a fractional number) resource units.Each server may be left unused at all, or be used for deploying exactly one of the services (but not for two of them simultaneously). The service should not use more resources than the server provides.Determine if it is possible to deploy both services using the given servers, and if yes, determine which servers should be used for deploying each of the services. | Input: ['6 8 163 5 2 9 8 7'] Output:['Yes3 21 2 65 4'] | [
4
] |
In the year of 30XX participants of some world programming championship live in a single large hotel. The hotel has n floors. Each floor has m sections with a single corridor connecting all of them. The sections are enumerated from 1 to m along the corridor, and all sections with equal numbers on different floors are located exactly one above the other. Thus, the hotel can be represented as a rectangle of height n and width m. We can denote sections with pairs of integers (i, j), where i is the floor, and j is the section number on the floor.The guests can walk along the corridor on each floor, use stairs and elevators. Each stairs or elevator occupies all sections (1, x), (2, x), ..., (n, x) for some x between 1 and m. All sections not occupied with stairs or elevators contain guest rooms. It takes one time unit to move between neighboring sections on the same floor or to move one floor up or down using stairs. It takes one time unit to move up to v floors in any direction using an elevator. You can assume you don't have to wait for an elevator, and the time needed to enter or exit an elevator is negligible.You are to process q queries. Each query is a question "what is the minimum time needed to go from a room in section (x_1, y_1) to a room in section (x_2, y_2)?" | Input: ['5 6 1 1 32531 1 5 61 3 5 43 3 5 3'] Output:['754'] | [
4
] |
Arkady decides to observe a river for n consecutive days. The river's water level on each day is equal to some real value.Arkady goes to the riverside each day and makes a mark on the side of the channel at the height of the water level, but if it coincides with a mark made before, no new mark is created. The water does not wash the marks away. Arkady writes down the number of marks strictly above the water level each day, on the i-th day this value is equal to mi.Define di as the number of marks strictly under the water level on the i-th day. You are to find out the minimum possible sum of di over all days. There are no marks on the channel before the first day. | Input: ['60 1 0 3 0 2'] Output:['6'] | [
2
] |
An atom of element X can exist in n distinct states with energies E1 < E2 < ... < En. Arkady wants to build a laser on this element, using a three-level scheme. Here is a simplified description of the scheme. Three distinct states i, j and k are selected, where i < j < k. After that the following process happens: initially the atom is in the state i, we spend Ek - Ei energy to put the atom in the state k, the atom emits a photon with useful energy Ek - Ej and changes its state to the state j, the atom spontaneously changes its state to the state i, losing energy Ej - Ei, the process repeats from step 1. Let's define the energy conversion efficiency as , i. e. the ration between the useful energy of the photon and spent energy.Due to some limitations, Arkady can only choose such three states that Ek - Ei ≤ U.Help Arkady to find such the maximum possible energy conversion efficiency within the above constraints. | Input: ['4 41 3 5 7'] Output:['0.5'] | [
2,
4
] |
There is a rectangular grid of n rows of m initially-white cells each.Arkady performed a certain number (possibly zero) of operations on it. In the i-th operation, a non-empty subset of rows Ri and a non-empty subset of columns Ci are chosen. For each row r in Ri and each column c in Ci, the intersection of row r and column c is coloured black.There's another constraint: a row or a column can only be chosen at most once among all operations. In other words, it means that no pair of (i, j) (i < j) exists such that or , where denotes intersection of sets, and denotes the empty set.You are to determine whether a valid sequence of operations exists that produces a given final grid. | Input: ['5 8.#.#..#......#...#.#..#.#.#....#.....#..'] Output:['Yes'] | [
2
] |
There is a number x initially written on a blackboard. You repeat the following action a fixed amount of times: take the number x currently written on a blackboard and erase it select an integer uniformly at random from the range [0, x] inclusive, and write it on the blackboard Determine the distribution of final number given the distribution of initial number and the number of steps. | Input: ['2 10 0 1'] Output:['332748118 332748118 332748118'] | [
3
] |
Alice has a very important message M consisting of some non-negative integers that she wants to keep secret from Eve. Alice knows that the only theoretically secure cipher is one-time pad. Alice generates a random key K of the length equal to the message's length. Alice computes the bitwise xor of each element of the message and the key (, where denotes the bitwise XOR operation) and stores this encrypted message A. Alice is smart. Be like Alice.For example, Alice may have wanted to store a message M = (0, 15, 9, 18). She generated a key K = (16, 7, 6, 3). The encrypted message is thus A = (16, 8, 15, 17).Alice realised that she cannot store the key with the encrypted message. Alice sent her key K to Bob and deleted her own copy. Alice is smart. Really, be like Alice.Bob realised that the encrypted message is only secure as long as the key is secret. Bob thus randomly permuted the key before storing it. Bob thinks that this way, even if Eve gets both the encrypted message and the key, she will not be able to read the message. Bob is not smart. Don't be like Bob.In the above example, Bob may have, for instance, selected a permutation (3, 4, 1, 2) and stored the permuted key P = (6, 3, 16, 7).One year has passed and Alice wants to decrypt her message. Only now Bob has realised that this is impossible. As he has permuted the key randomly, the message is lost forever. Did we mention that Bob isn't smart?Bob wants to salvage at least some information from the message. Since he is not so smart, he asks for your help. You know the encrypted message A and the permuted key P. What is the lexicographically smallest message that could have resulted in the given encrypted text?More precisely, for given A and P, find the lexicographically smallest message O, for which there exists a permutation π such that for every i.Note that the sequence S is lexicographically smaller than the sequence T, if there is an index i such that Si < Ti and for all j < i the condition Sj = Tj holds. | Input: ['38 4 1317 2 7'] Output:['10 3 28'] | [
2
] |
Alice likes snow a lot! Unfortunately, this year's winter is already over, and she can't expect to have any more of it. Bob has thus bought her a gift — a large snow maker. He plans to make some amount of snow every day. On day i he will make a pile of snow of volume Vi and put it in her garden.Each day, every pile will shrink a little due to melting. More precisely, when the temperature on a given day is Ti, each pile will reduce its volume by Ti. If this would reduce the volume of a pile to or below zero, it disappears forever. All snow piles are independent of each other. Note that the pile made on day i already loses part of its volume on the same day. In an extreme case, this may mean that there are no piles left at the end of a particular day.You are given the initial pile sizes and the temperature on each day. Determine the total volume of snow melted on each day. | Input: ['310 10 55 7 2'] Output:['5 12 4'] | [
4
] |
Alice and Bob begin their day with a quick game. They first choose a starting number X0 ≥ 3 and try to reach one million by the process described below. Alice goes first and then they take alternating turns. In the i-th turn, the player whose turn it is selects a prime number smaller than the current number, and announces the smallest multiple of this prime number that is not smaller than the current number.Formally, he or she selects a prime p < Xi - 1 and then finds the minimum Xi ≥ Xi - 1 such that p divides Xi. Note that if the selected prime p already divides Xi - 1, then the number does not change.Eve has witnessed the state of the game after two turns. Given X2, help her determine what is the smallest possible starting number X0. Note that the players don't necessarily play optimally. You should consider all possible game evolutions. | Input: ['14'] Output:['6'] | [
3
] |
Imp is really pleased that you helped him. But it you solve the last problem, his gladness would raise even more. Let's define for some set of integers as the number of pairs a, b in , such that: a is strictly less than b; a divides b without a remainder. You are to find such a set , which is a subset of {1, 2, ..., n} (the set that contains all positive integers not greater than n), that . | Input: ['3 3'] Output:['No'] | [
2
] |
Pushok the dog has been chasing Imp for a few hours already. Fortunately, Imp knows that Pushok is afraid of a robot vacuum cleaner. While moving, the robot generates a string t consisting of letters 's' and 'h', that produces a lot of noise. We define noise of string t as the number of occurrences of string "sh" as a subsequence in it, in other words, the number of such pairs (i, j), that i < j and and . The robot is off at the moment. Imp knows that it has a sequence of strings ti in its memory, and he can arbitrary change their order. When the robot is started, it generates the string t as a concatenation of these strings in the given order. The noise of the resulting string equals the noise of this concatenation.Help Imp to find the maximum noise he can achieve by changing the order of the strings. | Input: ['4sshhsshhhs'] Output:['18'] | [
2
] |
Imp is watching a documentary about cave painting. Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all , 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that: 1 ≤ i < j ≤ k, , where is the remainder of division x by y. | Input: ['4 4'] Output:['No'] | [
0
] |
Imp is in a magic forest, where xorangles grow (wut?) A xorangle of order n is such a non-degenerate triangle, that lengths of its sides are integers not exceeding n, and the xor-sum of the lengths is equal to zero. Imp has to count the number of distinct xorangles of order n to get out of the forest. Formally, for a given integer n you have to find the number of such triples (a, b, c), that: 1 ≤ a ≤ b ≤ c ≤ n; , where denotes the bitwise xor of integers x and y. (a, b, c) form a non-degenerate (with strictly positive area) triangle. | Input: ['6'] Output:['1'] | [
0
] |
Let's denote as L(x, p) an infinite sequence of integers y such that gcd(p, y) = 1 and y > x (where gcd is the greatest common divisor of two integer numbers), sorted in ascending order. The elements of L(x, p) are 1-indexed; for example, 9, 13 and 15 are the first, the second and the third elements of L(7, 22), respectively.You have to process t queries. Each query is denoted by three integers x, p and k, and the answer to this query is k-th element of L(x, p). | Input: ['37 22 17 22 27 22 3'] Output:['91315'] | [
0,
3,
4
] |
Let D(x) be the number of positive divisors of a positive integer x. For example, D(2) = 2 (2 is divisible by 1 and 2), D(6) = 4 (6 is divisible by 1, 2, 3 and 6).You are given an array a of n integers. You have to process two types of queries: REPLACE l r — for every replace ai with D(ai); SUM l r — calculate . Print the answer for each SUM query. | Input: ['7 66 4 1 10 3 2 42 1 72 4 51 3 52 4 41 5 72 1 7'] Output:['3013422'] | [
0
] |
Petya sometimes has to water his field. To water the field, Petya needs a tank with exactly V ml of water.Petya has got N tanks, i-th of them initially containing ai ml of water. The tanks are really large, any of them can contain any amount of water (no matter how large this amount is).Also Petya has got a scoop that can contain up to K ml of water (initially the scoop is empty). This scoop can be used to get some water from some tank, and after that pour it all into some tank (it is impossible to get water from multiple tanks without pouring it, or leave some water in the scoop when pouring it). When Petya tries to get some water from a tank, he gets min(v, K) water, where v is the current volume of water in the tank.Is it possible to obtain a tank with exactly V ml of water using these operations? If it is possible, print a sequence of operations that allows to do it. If there are multiple ways to obtain needed amount of water in some tank, print any of them. | Input: ['2 3 52 3'] Output:['YES1 2 1'] | [
2
] |
You have an array a consisting of n integers. Each integer from 1 to n appears exactly once in this array.For some indices i (1 ≤ i ≤ n - 1) it is possible to swap i-th element with (i + 1)-th, for other indices it is not possible. You may perform any number of swapping operations any order. There is no limit on the number of times you swap i-th element with (i + 1)-th (if the position is not forbidden).Can you make this array sorted in ascending order performing some sequence of swapping operations? | Input: ['61 2 5 3 4 601110'] Output:['YES'] | [
2,
3
] |
Given an integer x. Your task is to find out how many positive integers n (1 <=q n <=q x) satisfy n \cdot a^n \equiv b \quad (\textrm{mod}\;p), where a, b, p are all known constants. | Input: ['2 3 5 8'] Output:['2'] | [
3
] |
Suppose that you are in a campus and have to go for classes day by day. As you may see, when you hurry to a classroom, you surprisingly find that many seats there are already occupied. Today you and your friends went for class, and found out that some of the seats were occupied.The classroom contains n rows of seats and there are m seats in each row. Then the classroom can be represented as an n * m matrix. The character '.' represents an empty seat, while '*' means that the seat is occupied. You need to find k consecutive empty seats in the same row or column and arrange those seats for you and your friends. Your task is to find the number of ways to arrange the seats. Two ways are considered different if sets of places that students occupy differs. | Input: ['2 3 2**....'] Output:['3'] | [
0
] |
We consider a positive integer perfect, if and only if the sum of its digits is exactly 10. Given a positive integer k, your task is to find the k-th smallest perfect positive integer. | Input: ['1'] Output:['19'] | [
0,
4
] |
We often go to supermarkets to buy some fruits or vegetables, and on the tag there prints the price for a kilo. But in some supermarkets, when asked how much the items are, the clerk will say that a yuan for b kilos (You don't need to care about what "yuan" is), the same as a/b yuan for a kilo.Now imagine you'd like to buy m kilos of apples. You've asked n supermarkets and got the prices. Find the minimum cost for those apples.You can assume that there are enough apples in all supermarkets. | Input: ['3 51 23 41 3'] Output:['1.66666667'] | [
0,
2
] |
Eleven wants to choose a new name for herself. As a bunch of geeks, her friends suggested an algorithm to choose a name for her. Eleven wants her name to have exactly n characters. Her friend suggested that her name should only consist of uppercase and lowercase letters 'O'. More precisely, they suggested that the i-th letter of her name should be 'O' (uppercase) if i is a member of Fibonacci sequence, and 'o' (lowercase) otherwise. The letters in the name are numbered from 1 to n. Fibonacci sequence is the sequence f where f1 = 1, f2 = 1, fn = fn - 2 + fn - 1 (n > 2). As her friends are too young to know what Fibonacci sequence is, they asked you to help Eleven determine her new name. | Input: ['8'] Output:['OOOoOooO'] | [
0
] |
Will shares a psychic connection with the Upside Down Monster, so everything the monster knows, Will knows. Suddenly, he started drawing, page after page, non-stop. Joyce, his mom, and Chief Hopper put the drawings together, and they realized, it's a labeled tree! A tree is a connected acyclic graph. Will's tree has n vertices. Joyce and Hopper don't know what that means, so they're investigating this tree and similar trees. For each k such that 0 ≤ k ≤ n - 1, they're going to investigate all labeled trees with n vertices that share exactly k edges with Will's tree. Two labeled trees are different if and only if there's a pair of vertices (v, u) such that there's an edge between v and u in one tree and not in the other one.Hopper and Joyce want to know how much work they have to do, so they asked you to tell them the number of labeled trees with n vertices that share exactly k edges with Will's tree, for each k. The answer could be very large, so they only asked you to tell them the answers modulo 1000000007 = 109 + 7. | Input: ['31 21 3'] Output:['0 2 1 '] | [
3
] |
As Will is stuck in the Upside Down, he can still communicate with his mom, Joyce, through the Christmas lights (he can turn them on and off with his mind). He can't directly tell his mom where he is, because the monster that took him to the Upside Down will know and relocate him. Thus, he came up with a puzzle to tell his mom his coordinates. His coordinates are the answer to the following problem.A string consisting only of parentheses ('(' and ')') is called a bracket sequence. Some bracket sequence are called correct bracket sequences. More formally: Empty string is a correct bracket sequence. if s is a correct bracket sequence, then (s) is also a correct bracket sequence. if s and t are correct bracket sequences, then st (concatenation of s and t) is also a correct bracket sequence. A string consisting of parentheses and question marks ('?') is called pretty if and only if there's a way to replace each question mark with either '(' or ')' such that the resulting string is a non-empty correct bracket sequence.Will gave his mom a string s consisting of parentheses and question marks (using Morse code through the lights) and his coordinates are the number of pairs of integers (l, r) such that 1 ≤ l ≤ r ≤ |s| and the string slsl + 1... sr is pretty, where si is i-th character of s.Joyce doesn't know anything about bracket sequences, so she asked for your help. | Input: ['((?))'] Output:['4'] | [
2,
3
] |
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one. To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with . Give a value to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.For definitions of powers and lexicographical order see notes. | Input: ['23 5'] Output:['Yes3 3 2 1 0 '] | [
2,
3
] |
Jamie loves sleeping. One day, he decides that he needs to wake up at exactly hh: mm. However, he hates waking up, so he wants to make waking up less painful by setting the alarm at a lucky time. He will then press the snooze button every x minutes until hh: mm is reached, and only then he will wake up. He wants to know what is the smallest number of times he needs to press the snooze button.A time is considered lucky if it contains a digit '7'. For example, 13: 07 and 17: 27 are lucky, while 00: 48 and 21: 34 are not lucky.Note that it is not necessary that the time set for the alarm and the wake-up time are on the same day. It is guaranteed that there is a lucky time Jamie can set so that he can wake at hh: mm.Formally, find the smallest possible non-negative integer y such that the time representation of the time x·y minutes before hh: mm contains the digit '7'.Jamie uses 24-hours clock, so after 23: 59 comes 00: 00. | Input: ['311 23'] Output:['2'] | [
0,
3
] |
Let's call an array a of size n coprime iff gcd(a1, a2, ..., an) = 1, where gcd is the greatest common divisor of the arguments.You are given two numbers n and k. For each i (1 ≤ i ≤ k) you have to determine the number of coprime arrays a of size n such that for every j (1 ≤ j ≤ n) 1 ≤ aj ≤ i. Since the answers can be very large, you have to calculate them modulo 109 + 7. | Input: ['3 4'] Output:['82'] | [
3
] |
You are given two positive integer numbers a and b. Permute (change order) of the digits of a to construct maximal number not exceeding b. No number in input and/or output can start with the digit 0.It is allowed to leave a as it is. | Input: ['123222'] Output:['213'] | [
2
] |
You are given an array s of n non-negative integers.A 5-tuple of integers (a, b, c, d, e) is said to be valid if it satisfies the following conditions: 1 ≤ a, b, c, d, e ≤ n (sa | sb) & sc & (sd ^ se) = 2i for some integer i sa & sb = 0 Here, '|' is the bitwise OR, '&' is the bitwise AND and '^' is the bitwise XOR operation.Find the sum of f(sa|sb) * f(sc) * f(sd^se) over all valid 5-tuples (a, b, c, d, e), where f(i) is the i-th Fibonnaci number (f(0) = 0, f(1) = 1, f(i) = f(i - 1) + f(i - 2)).Since answer can be is huge output it modulo 109 + 7. | Input: ['21 2'] Output:['32'] | [
3
] |
Given a string s, process q queries, each having one of the following forms: 1 i c — Change the i-th character in the string to c. 2 l r y — Consider the substring of s starting at position l and ending at position r. Output the number of times y occurs as a substring in it. | Input: ['ababababa32 1 7 aba1 5 c2 1 7 aba'] Output:['31'] | [
0
] |
The Travelling Salesman spends a lot of time travelling so he tends to get bored. To pass time, he likes to perform operations on numbers. One such operation is to take a positive integer x and reduce it to the number of bits set to 1 in the binary representation of x. For example for number 13 it's true that 1310 = 11012, so it has 3 bits set and 13 will be reduced to 3 in one operation.He calls a number special if the minimum number of operations to reduce it to 1 is k.He wants to find out how many special numbers exist which are not greater than n. Please help the Travelling Salesman, as he is about to reach his destination!Since the answer can be large, output it modulo 109 + 7. | Input: ['1102'] Output:['3'] | [
0
] |
Edogawa Conan got tired of solving cases, and invited his friend, Professor Agasa, over. They decided to play a game of cards. Conan has n cards, and the i-th card has a number ai written on it.They take turns playing, starting with Conan. In each turn, the player chooses a card and removes it. Also, he removes all cards having a number strictly lesser than the number on the chosen card. Formally, if the player chooses the i-th card, he removes that card and removes the j-th card for all j such that aj < ai.A player loses if he cannot make a move on his turn, that is, he loses if there are no cards left. Predict the outcome of the game, assuming both players play optimally. | Input: ['34 5 7'] Output:['Conan'] | [
2
] |
Given an array a1, a2, ..., an of n integers, find the largest number in the array that is not a perfect square.A number x is said to be a perfect square if there exists an integer y such that x = y2. | Input: ['24 2'] Output:['2'] | [
0,
3
] |
You generate real numbers s1, s2, ..., sn as follows: s0 = 0; si = si - 1 + ti, where ti is a real number chosen independently uniformly at random between 0 and 1, inclusive. You are given real numbers x1, x2, ..., xn. You are interested in the probability that si ≤ xi is true for all i simultaneously.It can be shown that this can be represented as , where P and Q are coprime integers, and . Print the value of P·Q - 1 modulo 998244353. | Input: ['41.0023.0000004.0'] Output:['1'] | [
3
] |
You are given n positive integers a1, a2, ..., an.For every ai you need to find a positive integer ki such that the decimal notation of 2ki contains the decimal notation of ai as a substring among its last min(100, length(2ki)) digits. Here length(m) is the length of the decimal notation of m.Note that you don't have to minimize ki. The decimal notations in this problem do not contain leading zeros. | Input: ['282'] Output:['31'] | [
3
] |
There is a chess tournament in All-Right-City. n players were invited to take part in the competition. The tournament is held by the following rules: Initially, each player plays one game with every other player. There are no ties; After that, the organizers build a complete directed graph with players as vertices. For every pair of players there is exactly one directed edge between them: the winner of their game is the startpoint of this edge and the loser is the endpoint; After that, the organizers build a condensation of this graph. The condensation of this graph is an acyclic complete graph, therefore it has the only Hamiltonian path which consists of strongly connected components of initial graph A1 → A2 → ... → Ak. The players from the first component A1 are placed on the first places, the players from the component A2 are placed on the next places, and so on. To determine exact place of each player in a strongly connected component, all the procedures from 1 to 5 are repeated recursively inside each component, i.e. for every i = 1, 2, ..., k players from the component Ai play games with each other again, and so on; If a component consists of a single player, then he has no more rivals, his place is already determined and the process stops. The players are enumerated with integers from 1 to n. The enumeration was made using results of a previous tournament. It is known that player i wins player j (i < j) with probability p.You need to help to organize the tournament. Find the expected value of total number of games played by all the players. It can be shown that the answer can be represented as , where P and Q are coprime integers and . Print the value of P·Q - 1 modulo 998244353.If you are not familiar with any of the terms above, you can read about them here. | Input: ['31 2'] Output:['4'] | [
3
] |
You are preparing for an exam on scheduling theory. The exam will last for exactly T milliseconds and will consist of n problems. You can either solve problem i in exactly ti milliseconds or ignore it and spend no time. You don't need time to rest after solving a problem, either.Unfortunately, your teacher considers some of the problems too easy for you. Thus, he assigned an integer ai to every problem i meaning that the problem i can bring you a point to the final score only in case you have solved no more than ai problems overall (including problem i).Formally, suppose you solve problems p1, p2, ..., pk during the exam. Then, your final score s will be equal to the number of values of j between 1 and k such that k ≤ apj.You have guessed that the real first problem of the exam is already in front of you. Therefore, you want to choose a set of problems to solve during the exam maximizing your final score in advance. Don't forget that the exam is limited in time, and you must have enough time to solve all chosen problems. If there exist different sets of problems leading to the maximum final score, any of them will do. | Input: ['5 3003 1004 1504 802 902 300'] Output:['233 1 4'] | [
0,
2,
4
] |
A New Year party is not a New Year party without lemonade! As usual, you are expecting a lot of guests, and buying lemonade has already become a pleasant necessity.Your favorite store sells lemonade in bottles of n different volumes at different costs. A single bottle of type i has volume 2i - 1 liters and costs ci roubles. The number of bottles of each type in the store can be considered infinite.You want to buy at least L liters of lemonade. How many roubles do you have to spend? | Input: ['4 1220 30 70 90'] Output:['150'] | [
2
] |
The following problem is well-known: given integers n and m, calculate , where 2n = 2·2·...·2 (n factors), and denotes the remainder of division of x by y.You are asked to solve the "reverse" problem. Given integers n and m, calculate . | Input: ['442'] Output:['10'] | [
3
] |
Opposite to Grisha's nice behavior, Oleg, though he has an entire year at his disposal, didn't manage to learn how to solve number theory problems in the past year. That's why instead of Ded Moroz he was visited by his teammate Andrew, who solemnly presented him with a set of n distinct prime numbers alongside with a simple task: Oleg is to find the k-th smallest integer, such that all its prime divisors are in this set. | Input: ['32 3 57'] Output:['8'] | [
3,
4
] |
While Grisha was celebrating New Year with Ded Moroz, Misha gifted Sasha a small rectangular pond of size n × m, divided into cells of size 1 × 1, inhabited by tiny evil fishes (no more than one fish per cell, otherwise they'll strife!).The gift bundle also includes a square scoop of size r × r, designed for fishing. If the lower-left corner of the scoop-net is located at cell (x, y), all fishes inside the square (x, y)...(x + r - 1, y + r - 1) get caught. Note that the scoop-net should lie completely inside the pond when used.Unfortunately, Sasha is not that skilled in fishing and hence throws the scoop randomly. In order to not frustrate Sasha, Misha decided to release k fishes into the empty pond in such a way that the expected value of the number of caught fishes is as high as possible. Help Misha! In other words, put k fishes in the pond into distinct cells in such a way that when the scoop-net is placed into a random position among (n - r + 1)·(m - r + 1) possible positions, the average number of caught fishes is as high as possible. | Input: ['3 3 2 3'] Output:['2.0000000000'] | [
2
] |
A lot of students spend their winter holidays productively. Vlad has advanced very well in doing so! For three days already, fueled by salads and tangerines — the leftovers from New Year celebration — he has been calibrating his rating in his favorite MOBA game, playing as a hero named Perun.Perun has an ultimate ability called "Thunderwrath". At the instant of its activation, each enemy on the map (n of them in total) loses health points as a single-time effect. It also has a restriction: it can only activated when the moment of time is an integer. The initial bounty for killing an enemy is . Additionally, it increases by each second. Formally, if at some second t the ability is activated and the i-th enemy is killed as a result (i.e. his health drops to zero or lower), Vlad earns units of gold.Every enemy can receive damage, as well as be healed. There are multiple ways of doing so, but Vlad is not interested in details. For each of n enemies he knows: — maximum number of health points for the i-th enemy; — initial health of the enemy (on the 0-th second); — the amount of health the i-th enemy can regenerate per second. There also m health updates Vlad knows about: — time when the health was updated; — the enemy whose health was updated; — updated health points for enemyj. Obviously, Vlad wants to maximize his profit. If it's necessary, he could even wait for years to activate his ability at the right second. Help him determine the exact second (note that it must be an integer) from 0 (inclusively) to + ∞ so that a single activation of the ability would yield Vlad the maximum possible amount of gold, and print this amount. | Input: ['3 21000 10 5070 5 590 70 1110 20 220 2 1030 3 10'] Output:['3000'] | [
0,
2
] |
You are given an unweighted tree with n vertices. Then n - 1 following operations are applied to the tree. A single operation consists of the following steps: choose two leaves; add the length of the simple path between them to the answer; remove one of the chosen leaves from the tree. Initial answer (before applying operations) is 0. Obviously after n - 1 such operations the tree will consist of a single vertex. Calculate the maximal possible answer you can achieve, and construct a sequence of operations that allows you to achieve this answer! | Input: ['31 21 3'] Output:['32 3 32 1 1'] | [
2
] |
Let's suppose you have an array a, a stack s (initially empty) and an array b (also initially empty).You may perform the following operations until both a and s are empty: Take the first element of a, push it into s and remove it from a (if a is not empty); Take the top element from s, append it to the end of array b and remove it from s (if s is not empty). You can perform these operations in arbitrary order.If there exists a way to perform the operations such that array b is sorted in non-descending order in the end, then array a is called stack-sortable.For example, [3, 1, 2] is stack-sortable, because b will be sorted if we perform the following operations: Remove 3 from a and push it into s; Remove 1 from a and push it into s; Remove 1 from s and append it to the end of b; Remove 2 from a and push it into s; Remove 2 from s and append it to the end of b; Remove 3 from s and append it to the end of b. After all these operations b = [1, 2, 3], so [3, 1, 2] is stack-sortable. [2, 3, 1] is not stack-sortable.You are given k first elements of some permutation p of size n (recall that a permutation of size n is an array of size n where each integer from 1 to n occurs exactly once). You have to restore the remaining n - k elements of this permutation so it is stack-sortable. If there are multiple answers, choose the answer such that p is lexicographically maximal (an array q is lexicographically greater than an array p iff there exists some integer k such that for every i < k qi = pi, and qk > pk). You may not swap or change any of first k elements of the permutation.Print the lexicographically maximal permutation p you can obtain.If there exists no answer then output -1. | Input: ['5 33 2 1'] Output:['3 2 1 5 4 '] | [
2
] |
A permutation of size n is an array of size n such that each integer from 1 to n occurs exactly once in this array. An inversion in a permutation p is a pair of indices (i, j) such that i > j and ai < aj. For example, a permutation [4, 1, 3, 2] contains 4 inversions: (2, 1), (3, 1), (4, 1), (4, 3).You are given a permutation a of size n and m queries to it. Each query is represented by two indices l and r denoting that you have to reverse the segment [l, r] of the permutation. For example, if a = [1, 2, 3, 4] and a query l = 2, r = 4 is applied, then the resulting permutation is [1, 4, 3, 2].After each query you have to determine whether the number of inversions is odd or even. | Input: ['31 2 321 22 3'] Output:['oddeven'] | [
0,
3
] |
Mishka is decorating the Christmas tree. He has got three garlands, and all of them will be put on the tree. After that Mishka will switch these garlands on.When a garland is switched on, it periodically changes its state — sometimes it is lit, sometimes not. Formally, if i-th garland is switched on during x-th second, then it is lit only during seconds x, x + ki, x + 2ki, x + 3ki and so on.Mishka wants to switch on the garlands in such a way that during each second after switching the garlands on there would be at least one lit garland. Formally, Mishka wants to choose three integers x1, x2 and x3 (not necessarily distinct) so that he will switch on the first garland during x1-th second, the second one — during x2-th second, and the third one — during x3-th second, respectively, and during each second starting from max(x1, x2, x3) at least one garland will be lit.Help Mishka by telling him if it is possible to do this! | Input: ['2 2 3'] Output:['YES'] | [
0
] |
It's New Year's Eve soon, so Ivan decided it's high time he started setting the table. Ivan has bought two cakes and cut them into pieces: the first cake has been cut into a pieces, and the second one — into b pieces.Ivan knows that there will be n people at the celebration (including himself), so Ivan has set n plates for the cakes. Now he is thinking about how to distribute the cakes between the plates. Ivan wants to do it in such a way that all following conditions are met: Each piece of each cake is put on some plate; Each plate contains at least one piece of cake; No plate contains pieces of both cakes. To make his guests happy, Ivan wants to distribute the cakes in such a way that the minimum number of pieces on the plate is maximized. Formally, Ivan wants to know the maximum possible number x such that he can distribute the cakes according to the aforementioned conditions, and each plate will contain at least x pieces of cake.Help Ivan to calculate this number x! | Input: ['5 2 3'] Output:['1'] | [
0,
4
] |
Petya has n positive integers a1, a2, ..., an. His friend Vasya decided to joke and replaced all digits in Petya's numbers with a letters. He used the lowercase letters of the Latin alphabet from 'a' to 'j' and replaced all digits 0 with one letter, all digits 1 with another letter and so on. For any two different digits Vasya used distinct letters from 'a' to 'j'.Your task is to restore Petya's numbers. The restored numbers should be positive integers without leading zeros. Since there can be multiple ways to do it, determine the minimum possible sum of all Petya's numbers after the restoration. It is guaranteed that before Vasya's joke all Petya's numbers did not have leading zeros. | Input: ['3abdeaj'] Output:['47'] | [
2,
3
] |
Petya has equal wooden bars of length n. He wants to make a frame for two equal doors. Each frame has two vertical (left and right) sides of length a and one top side of length b. A solid (i.e. continuous without breaks) piece of bar is needed for each side.Determine a minimal number of wooden bars which are needed to make the frames for two doors. Petya can cut the wooden bars into any parts, but each side of each door should be a solid piece of a wooden bar (or a whole wooden bar). | Input: ['812'] Output:['1'] | [
2
] |
A frog lives on the axis Ox and needs to reach home which is in the point n. She starts from the point 1. The frog can jump to the right at a distance not more than d. So, after she jumped from the point x she can reach the point x + a, where a is an integer from 1 to d.For each point from 1 to n is known if there is a lily flower in it. The frog can jump only in points with a lilies. Guaranteed that there are lilies in the points 1 and n.Determine the minimal number of jumps that the frog needs to reach home which is in the point n from the point 1. Consider that initially the frog is in the point 1. If the frog can not reach home, print -1. | Input: ['8 410010101'] Output:['2'] | [
2
] |
You are given a program you want to execute as a set of tasks organized in a dependency graph. The dependency graph is a directed acyclic graph: each task can depend on results of one or several other tasks, and there are no directed circular dependencies between tasks. A task can only be executed if all tasks it depends on have already completed.Some of the tasks in the graph can only be executed on a coprocessor, and the rest can only be executed on the main processor. In one coprocessor call you can send it a set of tasks which can only be executed on it. For each task of the set, all tasks on which it depends must be either already completed or be included in the set. The main processor starts the program execution and gets the results of tasks executed on the coprocessor automatically.Find the minimal number of coprocessor calls which are necessary to execute the given program. | Input: ['4 30 1 0 10 11 22 3'] Output:['2'] | [
2
] |
You are given a set of points on a straight line. Each point has a color assigned to it. For point a, its neighbors are the points which don't have any other points between them and a. Each point has at most two neighbors - one from the left and one from the right.You perform a sequence of operations on this set of points. In one operation, you delete all points which have a neighbor point of a different color than the point itself. Points are deleted simultaneously, i.e. first you decide which points have to be deleted and then delete them. After that you can perform the next operation etc. If an operation would not delete any points, you can't perform it.How many operations will you need to perform until the next operation does not have any points to delete? | Input: ['aabb'] Output:['2'] | [
2
] |
You are given an integer N. Consider all possible segments on the coordinate axis with endpoints at integer points with coordinates between 0 and N, inclusive; there will be of them.You want to draw these segments in several layers so that in each layer the segments don't overlap (they might touch at the endpoints though). You can not move the segments to a different location on the coordinate axis. Find the minimal number of layers you have to use for the given N. | Input: ['2'] Output:['2'] | [
3
] |
The preferred way to generate user login in Polygon is to concatenate a prefix of the user's first name and a prefix of their last name, in that order. Each prefix must be non-empty, and any of the prefixes can be the full name. Typically there are multiple possible logins for each person.You are given the first and the last name of a user. Return the alphabetically earliest login they can get (regardless of other potential Polygon users).As a reminder, a prefix of a string s is its substring which occurs at the beginning of s: "a", "ab", "abc" etc. are prefixes of string "{abcdef}" but "b" and 'bc" are not. A string a is alphabetically earlier than a string b, if a is a prefix of b, or a and b coincide up to some position, and then a has a letter that is alphabetically earlier than the corresponding letter in b: "a" and "ab" are alphabetically earlier than "ac" but "b" and "ba" are alphabetically later than "ac". | Input: ['harry potter'] Output:['hap'] | [
0,
2
] |
Let S(n) denote the number that represents the digits of n in sorted order. For example, S(1) = 1, S(5) = 5, S(50394) = 3459, S(353535) = 333555.Given a number X, compute modulo 109 + 7. | Input: ['21'] Output:['195'] | [
3
] |
Roy and Biv have a set of n points on the infinite number line.Each point has one of 3 colors: red, green, or blue.Roy and Biv would like to connect all the points with some edges. Edges can be drawn between any of the two of the given points. The cost of an edge is equal to the distance between the two points it connects.They want to do this in such a way that they will both see that all the points are connected (either directly or indirectly).However, there is a catch: Roy cannot see the color red and Biv cannot see the color blue.Therefore, they have to choose the edges in such a way that if all the red points are removed, the remaining blue and green points are connected (and similarly, if all the blue points are removed, the remaining red and green points are connected).Help them compute the minimum cost way to choose edges to satisfy the above constraints. | Input: ['41 G5 R10 B15 G'] Output:['23'] | [
2
] |
You are given an integer m.Let M = 2m - 1.You are also given a set of n integers denoted as the set T. The integers will be provided in base 2 as n binary strings of length m.A set of integers S is called "good" if the following hold. If , then . If , then All elements of S are less than or equal to M. Here, and refer to the bitwise XOR and bitwise AND operators, respectively.Count the number of good sets S, modulo 109 + 7. | Input: ['5 3110100010111000'] Output:['4'] | [
3
] |
You are given three integers k, pa and pb.You will construct a sequence with the following algorithm: Initially, start with the empty sequence. Each second, you do the following. With probability pa / (pa + pb), add 'a' to the end of the sequence. Otherwise (with probability pb / (pa + pb)), add 'b' to the end of the sequence.You stop once there are at least k subsequences that form 'ab'. Determine the expected number of times 'ab' is a subsequence in the resulting sequence. It can be shown that this can be represented by P / Q, where P and Q are coprime integers, and . Print the value of . | Input: ['1 1 1'] Output:['2'] | [
3
] |
Carol is currently curling.She has n disks each with radius r on the 2D plane. Initially she has all these disks above the line y = 10100.She then will slide the disks towards the line y = 0 one by one in order from 1 to n. When she slides the i-th disk, she will place its center at the point (xi, 10100). She will then push it so the disk’s y coordinate continuously decreases, and x coordinate stays constant. The disk stops once it touches the line y = 0 or it touches any previous disk. Note that once a disk stops moving, it will not move again, even if hit by another disk. Compute the y-coordinates of centers of all the disks after all disks have been pushed. | Input: ['6 25 5 6 8 3 12'] Output:['2 6.0 9.87298334621 13.3370849613 12.5187346573 13.3370849613'] | [
0,
3
] |
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