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>\n\nOkay, let's try to figure out how to solve this problem. The problem seems a bit complex, so I need to break it down step by step.\n\nFirst, the problem involves a tree where some nodes are energetic. These energetic nodes contribute energy to themselves and their neighbors each second. The energy added in the i-t... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem carefully.\n\nSo the problem is about computing the sum of certain Fibonacci-like numbers for all possible pairs of A and B elements. The final result is the sum of fib[N] for every possible pair (A[i], B[j]). Then we take modulo 1e9+7.\n\nThe ... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem statement carefully.\n\nSo, Chef is in a 2D maze with N rows and M columns. He needs to find a magical path. The conditions for a magical path are:\n\n1. The path starts at (a,b) and ends at (c,d) such that |a -c| + |b -d| = 1. So the start and... |
>\n\nOkay, let's see. The problem is about a game played on a tree where two players take turns removing leaf nodes. The special node x determines the winner. We need to find out who wins if both play optimally.\n\nHmm. So the key here is to figure out under what conditions the first player (Ayush) can force a win. Let... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem carefully.\n\nThe task is to find the minimum number of changes required to make a given string 'a'-good. An 'a'-good string is defined recursively. Let's break down the conditions.\n\nFirst, the definition of a c-good string:\n\n1. If the leng... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem carefully.\n\nSo, the problem is about arranging a stack of books in such a way that when Jaehyun reads them according to a given sequence over m days, the total weight he has to lift is minimized. Each time he reads a book, he lifts all the bo... |
>\n\nOkay, let's see. I need to solve this problem where there are two heaps in a Nim game, but with some shortcut positions that make the current player lose instantly. The task is to determine for each given initial position whether the starting player can win, assuming both play optimally.\n\nFirst, let's understand... |
>\n\nOkay, let's see. I need to solve this problem where I have to check if the concatenated children's names form a substring of any permutation of the parents' combined names. Hmm. So the main steps would be: first, check if the combined children's characters even match the parents' characters (count-wise), and then ... |
>\n\nOkay, let's try to solve this problem. Hmm. The problem says we need to check if the given happiness indexes for all cities are possible based on the movement of people and their mood changes. \n\nSo, the setup is a tree structure with cities connected as a tree, rooted at the capital (city 1). Each person lives i... |
>\n\nOkay, I need to solve this programming problem. Let's start by understanding what the problem is asking.\n\nSo, the problem is about splitting students into two teams such that each team has an equal number of students, and no two archenemies are in the same team. If it's impossible, some students have to sit out.... |
>\n\nOkay, let's try to figure out how to solve this problem. So the problem is, given two numbers s (the sum of a and b) and x (the bitwise XOR of a and b), we need to find the number of ordered pairs (a, b) that satisfy these conditions. Hmm.\n\nWait, I remember there's a relation between sum and XOR. Let me think. O... |
>\n\nOkay, let's see. The problem is about determining whether Monocarp's character can move from the starting position (1,1) to the ending position (2,n) in a grid that's 2 rows by n columns. The movement is allowed to adjacent cells, including diagonally adjacent ones. But some cells have traps (marked as '1'), and i... |
>\n\nOkay, so I need to solve this programming problem. Let's read the problem carefully.\n\nThe problem is about scheduling flights for jury members to be in the Metropolis (city 0) for exactly k consecutive days. All jury members (from cities 1 to n) must arrive before these k days start and leave after they end. The... |
>\n\nOkay, let's tackle this problem. Hmm, the task is to find the number of regular bracket sequences of length 2n that contain a given substring s. And the result has to be modulo 1e9+7. \n\nFirst, I need to understand what a regular bracket sequence is. Oh right, it's a balanced sequence where every opening bracket ... |
>\n\nOkay, let's try to understand this problem. We need to find the minimum number of cats K such that Tom can catch Jerry no matter how Jerry moves. The problem statement is a bit complex, so let's break it down.\n\nFirst, the graph has a special property: every simple cycle with at least four vertices has a chord. T... |
>\n\nOkay, let's see. I need to solve this problem where for each query, I have to determine if the bitwise AND of a subarray from L to R is even or odd. Hmm.\n\nFirst, I remember that the bitwise AND of numbers is even if at least one of the numbers in the range has the least significant bit (LSB) as 0. Because the AN... |
>\n\nOkay, let's see. I need to solve this programming problem. Let's read the problem carefully.\n\nSo, the problem is about a garland of colored bulbs. The bulbs can be red (R), blue (B), yellow (Y), green (G), or dead (!). The key thing is that the garland is constructed such that any four consecutive bulbs are all ... |
>\n\nOkay, I need to solve this problem where I have to find the minimum number of p-binary numbers that sum up to n. Let's start by understanding the problem.\n\nSo, a p-binary number is of the form 2^x + p, where x is a non-negative integer. The sum of several such numbers should equal n. My task is to find the small... |
>\n\nOkay, let's try to understand this problem. So, we have a tree rooted at node 0, and each day, the value of each node is updated based on the XOR of all the nodes in its subtree from the previous day. The process starts from the root and then proceeds recursively to the children. For each query Δ, we need to compu... |
>\n\nOkay, I need to solve this problem where Samu wants to choose the minimum number of dishes such that every friend has at least one dish they like. Let's see the problem again.\n\nSo the input is T test cases. For each test case, there's N friends and K dishes. Each friend has a string of K characters (0s and 1s) i... |
>\n\nOkay, let's see. The problem is about dividing a set of distinct integers into two groups A and B with certain conditions. Hmm. The conditions are that if a number x is in A, then a - x must also be in A. Similarly for B with b - x. So each group must be closed under the operation of taking the complement with res... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem carefully.\n\nSo, the problem is about building a new house in Flatville. The existing houses are on the Ox-axis, they are squares with their centers on the axis. The new house must also be a square with its center on Ox, side length t, and it ... |
>\n\nOkay, I need to solve this problem where I have to check if a social network is \"reasonable\" according to the given condition. The condition is that for every three distinct members X, Y, Z, if X is friends with Y and Y is friends with Z, then X must also be friends with Z. So basically, the friends graph needs ... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem statement carefully.\n\nThe problem is about trees and finding the maximum length of a \"cool\" sequence. A cool sequence is a list of vertices where each consecutive pair's distance is exactly their step index. For example, the first step (bet... |
>\n\nOkay, let's tackle this problem. Hmm. So the goal is to find the minimum coins needed to get all voters to vote for us. Each voter can be either bought with coins or convinced if at least m_i others are already voting. And this process happens in steps, where each step adds more voters based on the current set. \n... |
>\n\nOkay, so I need to determine if a given social network is \"reasonable\" according to the problem's condition. The condition is that for every three distinct members X, Y, Z, if X-Y and Y-Z are friends, then X-Z must also be friends. Hmm, that sounds a lot like checking if the graph is a collection of cliques. Bec... |
>\n\nOkay, let's see. The problem is about Vitaly trying to get through a series of rooms, each requiring a key to open the door to the next room. The keys are in the rooms, but once he uses a key, it's gone. So he needs to collect keys as he goes, but sometimes he might need to buy some beforehand. We need to find the... |
>\n\nOkay, let's see. I need to solve this problem where for each segment, I have to find how many other segments are completely contained within it. The input is a bunch of segments, and none of their endpoints coincide. So each segment's start and end are unique in the list. Hmm.\n\nFirst, I need to figure out an eff... |
>\n\nOkay, let's see. I need to figure out where to place the chip on the roulette table. The problem says the chip must be entirely within a square, not on any edges or corners. So each square on the roulette is a betting area, right? The chip can't overlap edges or be on shared corners. So the center of the chip must... |
>\n\nOkay, let's try to solve this problem. Hmm, the task is to rearrange the array such that the beauty, which is the minimum of the LIS of the array and the LIS of its reversed version, is maximized. So we need to find the optimal arrangement where this minimum is as large as possible.\n\nFirst, I need to understand ... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem carefully and understand what's required.\n\nThe problem is about finding the number of stable blocks of a certain order K within a given range [L, R] of days. A stable block is a maximal consecutive sequence of the same price. The order K mean... |
>\n\nOkay, let's tackle this problem. Hmm. The goal is to compute the expected number of hearts in a randomly chosen rectangle from an N x M grid. The expectation is the sum over all possible rectangles of (probability of the rectangle) multiplied by the number of hearts it contains. But since each heart's inclusion is... |
>\n\nOkay, let's tackle this problem. Hmm, the problem is about counting the number of paths from various starting points S to a target B. Each chef can only trust chefs with higher IDs, so the graph is directed and acyclic. Oh right, the trust is one-way and only to higher IDs. So the structure is like a DAG where edg... |
>\n\nOkay, let's see. I need to find an integer X greater than N such that X is not a multiple of N, and the absolute difference between the GCD and LCM of N and X is as small as possible. Hmm. The problem is to minimize |gcd(N,X) - lcm(N,X)|. Oh right, and X has to be greater than N and not a multiple of it.\n\nFirst,... |
>\n\nOkay, let's tackle this problem. Hmm, the task is to find an array of N elements such that exactly E subarrays have even sum and O have odd sum. And if not possible, output -1. The constraints are E + O equals the total number of subarrays, which is N*(N+1)/2. So the input will always satisfy that, as per the prob... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem carefully.\n\nThe problem is about finding the lexicographically smallest binary string t of length k such that it's \"bit similar\" to all substrings of s of length k. Bit similar means that for each substring of s of length k, there's at leas... |
>\n\nOkay, let's try to figure out this problem. So, the problem is about calculating the expected length of Bob's array after he plays his game. The array is shuffled by Alice, and then Bob chooses indices one by one, and keeps the number only if it's the first or larger than all previous ones. The expectation is over... |
>\n\nOkay, let's tackle this problem. Let's read through the problem statement carefully.\n\nSo the task is to process multiple queries on a string P. Each query gives us two characters a and b, and a range L to R. We need to find the number of substrings that start with a, end with b, have different start and end char... |
>\n\nOkay, I need to solve this problem where I have to find the lexicographically smallest permutation possible by swapping elements according to the given adjacency matrix. Let's think through this step by step.\n\nFirst, let's understand the problem. We have a permutation P of size K. We can swap elements i and j an... |
>\n\nOkay, I need to solve this problem where I have to find the number of arrays of size N with elements between 1 and M such that every pair of elements has a GCD of 1. And since the answer can be large, I have to return it modulo 1e9+7. Hmm.\n\nLet me think. The constraints are T up to 10, N up to 1e5, M up to 100. ... |
>\n\nOkay, let's tackle this problem. Hmm, the problem requires us to count the number of ways to close roads such that the remaining roads form a spanning tree with exactly k dead ends. Oh right, a dead end is a node with degree 1. So, the spanning tree must have exactly k nodes of degree 1.\n\nFirst, let's understand... |
>\n\nOkay, let's try to figure out how to solve this problem. So the problem is, given an array A and a target Y, we need to find the minimal non-negative integer X such that when we append X to A, the bitwise OR of all elements (including X) equals Y. If it's not possible, we output -1.\n\nHmm. Let's start by understa... |
>\n\nOkay, let's see. The problem is about a tree where each node represents a vertex, and Limak can jump from a vertex to any other vertex within distance at most k. We need to calculate the sum of the minimal number of jumps required for all pairs (s, t) where s < t. \n\nHmm. So for each pair of nodes s and t, the mi... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem carefully.\n\nSo, the problem is about finding the maximum path sum from (x1, y1) to (x2, y2) in an infinite matrix where movement is only right or down. The matrix is filled in a certain way. The initial cell (1,1) has value 1. Then, how are t... |
>\n\nOkay, let's try to figure out this problem. Hmm. So, the problem is about a graph where nodes are integers, and edges exist between two nodes if their values are not coprime. Then, for each query, we need to find the minimum number of new nodes we have to add to connect a_s and a_t. The new nodes are created by ta... |
>\n\nOkay, let's see. I need to find the total duration of the game based on the given N, A, and B. Hmm. The problem says it's a 3+2 blitz chess match. So each player starts with a minutes, which is 3 minutes, right? So that's 180 seconds. And each move adds b=2 seconds. Wait, no, the a is 3 minutes, so 3*60=180 second... |
>\n\nOkay, let's tackle this problem. Hmm. So the task is to find the maximum number of friends that can be made happy by choosing the right times to change the handle. Let me read the problem statement again to make sure I understand it.\n\nSo, each event is either type 1 (a chance to change the handle) or type 2 (a f... |
>\n\nOkay, let's tackle this problem. Hmm, the task is to determine for each query substring whether Sereja's algorithm can possibly terminate. If there's any possible way that after some permutations of three-character substrings, the algorithm stops, then we output YES. Otherwise, NO.\n\nFirst, I need to understand t... |
>\n\nOkay, I need to solve this problem where I have to determine if a given word is a mirror word. Let's think about what a mirror word is. From the problem statement, when the word is written in this specific sans-serif font and viewed in a mirror, it should look exactly the same as the original. So, the reflection o... |
>\n\nOkay, let's see. I need to find a binary string that matches the given a00, a01, a10, a11 values. Hmm. Let's start by understanding what these a values represent. Oh right, axy is the number of subsequences of length 2 in the string equal to x followed by y. So for example, in the string \"0110\", the pairs would ... |
>\n\nOkay, let's see. I need to find the minimum number of weapons a kid cyborg can have when distributing K weapons among N kids, with the rule that the difference between the maximum and minimum is at most 1. Hmm.\n\nSo the problem is to distribute K weapons such that after distribution, the maximum and minimum diffe... |
>\n\nOkay, let's see. The problem is to find the minimal number of digits 1 in a sum of numbers composed of only 1s that add up to a given number n. Hmm. For example, in the sample input 121, the solution is 6 digits. The example uses 111 + 11 -1, which totals 121, and the sum of digits is 3 (from 111) + 2 (from 11) + ... |
>\n\nOkay, let's see. The problem is about determining the winner of a game between two players who take turns incrementing elements of an array. The losing condition is when after incrementing, there's no permutation p of 1..N such that each a_i ≤ p_i. Both play optimally, so we need to find if the first player can fo... |
>\n\nOkay, I need to write a Python function that reads input, sorts an array, and outputs the sorted array. Let's see. The input is a single line of space-separated integers. The first number is the size n, followed by n elements. So the input format is something like, for example, \"3 3 1 2\" where 3 is the size, and... |
>\n\nOkay, let's try to solve this problem. Hmm, the problem statement is a bit complicated. Let's read through it again carefully.\n\nSo, Sereja has two arrays a and b. He does two operations: first, shuffles array b randomly (so all permutations are equally likely). Then, he merges a and b into a new array a using a ... |
>\n\nOkay, let's tackle this problem. So, the task is to find directions for four bots so that after moving some integer distance, they form a square with sides parallel to the axes, and each corner has exactly one bot. Also, we need to minimize the maximum distance any bot moves. Hmm.\n\nFirst, let's understand the sq... |
>\n\nOkay, let's see. The problem is about a tree where each node has a value a_i, and each edge has a weight. We need to find for each node v, how many nodes u in its subtree are controlled by v. Controlled here means that the sum of the edge weights along the path from v to u (which is the distance between them in th... |
>\n\nOkay, let's tackle this problem. Hmm, so the task is to find an athlete who is superior to all others. An athlete x is superior to y if x has a better rank (lower number) in at least 3 of the 5 marathons. We need to find any such athlete or return -1 if none exists.\n\nFirst, I need to think about how to efficient... |
>\n\nOkay, let's see. I need to find three numbers a, b, c where a < b < c, all between l and r inclusive. The conditions are that gcd(a, b) = 1, gcd(b, c) = 1, but gcd(a, c) is not 1. And if such a triplet doesn't exist, output -1.\n\nHmm. The challenge is to find such triplet efficiently given that the range l to r c... |
>\n\nOkay, so I have this problem where I need to calculate the sum of the cubes of all possible subarray sums of an array. The problem says that for each test case, given an array A of length N, compute the sum over all i and j (with j >= i) of F(i,j)^3, where F(i,j) is the sum of elements from index i to j. And then ... |
>\n\nOkay, let's see. The problem is to find the minimum cost Chef needs to get the lex smallest binary string by using at most one free prefix reverse and any number of swaps that cost 1 each. Hmm.\n\nSo, first, the key is that type 2 operation (reverse a prefix) can be done at most once. So the plan is to consider al... |
>\n\nOkay, I need to solve this problem where Chef can remove all cards from a row based on certain rules. Let's understand the problem step by step.\n\nSo the rules are:\n- Each card can be removed only if it's face up (1).\n- When you remove a card, its adjacent cards (left and right, if they exist) are flipped. So i... |
>\n\nOkay, let's tackle this problem. Hmm, the task is to find a string Z that maximizes the sum of the Hamming distances between X and Z, and Y and Z. Also, if there are multiple Zs with the maximum sum, we need the lex smallest one.\n\nFirst, let's understand what the sum of the Hamming distances represents. For each... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem statement carefully.\n\nThe problem is about a game between Jeff and Furik. They take turns swapping elements in a permutation until it's sorted. Jeff wants to minimize the expected number of moves. I have to compute this minimal expected value... |
>\n\nOkay, let's try to figure out how to solve this problem. So the task is to find the maximum possible k such that there's a row permutation of the matrix that makes the traversal sequence have adjacent elements differing by at least k. Hmm.\n\nFirst, I need to understand the problem structure. The matrix has n rows... |
>\n\nOkay, I need to solve this problem where I have to compute the sum of the GCDs of all cells in a K-dimensional hyperrectangle. The constraints are pretty tight, especially since K can be up to 500 and each dimension up to 1e5. So a brute force approach is definitely out of the question. Let's think about how to ap... |
>\n\nOkay, I need to solve this problem where Koa has to transform string A into string B using the least number of moves. The moves involve selecting positions with the same character and changing them all to a higher character. Let's think through this step by step.\n\nFirst, let's understand the problem. For each po... |
>\n\nOkay, let's try to figure out how to solve this problem. Hmm, the problem is about Hilbert's Hotel and determining if after shuffling the guests, every room still has exactly one guest. So, the key is to check whether the shuffling is a permutation of the integers, right? That is, the function mapping each room k ... |
>\n\nOkay, let's tackle this problem. Hmm, the task is to assign labels to the vertices such that the edge labels (which are the number of common divisors between the labels of their endpoints) match the given matrix. Oh right, and each vertex must have a distinct label from 1 to N. Wait, no, the problem says \"distinc... |
>\n\nOkay, let's see. I need to solve this problem where I have to find the shortest path between two railway stations based on the given connections. The input is a bunch of stations and their direct distances, and for each query, I have to output the minimum distance. \n\nHmm, first, the problem is about finding the ... |
>\n\nOkay, let's try to solve this problem. So the task is to find the minimum number of operations needed to sort a permutation using the described operation. The operation allows us to pick two elements, remove them, then place the minimum of them at the beginning and the maximum at the end. Hmm.\n\nFirst, I need to ... |
>\n\nOkay, let's see. The problem is about processing a series of commands where each command can either update an array or execute a range of previous commands. The challenge is to handle this efficiently given the constraints, especially since n and m can be up to 1e5, which is pretty big. So a naive approach of simu... |
>\n\nOkay, let's see. The problem is about determining if a given string can be rearranged into a Palpal string. A Palpal string is one that can be divided into contiguous palindromic substrings, each of length at least 2. So, each part is a palindrome of two or more characters.\n\nHmm. The key is that after rearrangem... |
>\n\nOkay, so I have this problem where I need to find the minimum cost to turn a binary string into all ones using two operations: reverse a substring (cost x) or flip a substring (cost y). Hmm, let's think.\n\nFirst, reversing a substring doesn't actually change the structure of the zeros and ones in terms of groupin... |
>\n\nOkay, I need to solve this programming problem. Let me read the problem statement carefully and understand what's required.\n\nThe task is to determine if a given sequence of words is a valid sentence according to Petya's language rules. A sentence is either a single valid word or a statement that follows certain ... |
>\n\nOkay, let's tackle this problem. So, the task is to find the final username after a series of deletion operations. Let's understand the problem step by step.\n\nThe initial username is t, which is formed by concatenating k copies of string s. So if s is 'bac' and k is 2, then t becomes 'bacbac'. Then, there are n ... |
>\n\nOkay, I need to solve this problem where I have to find the number of pairs (i,j) in an array such that (A_i XOR A_j) AND X equals zero. Let's think about what this condition really means.\n\nFirst, let's parse the condition ((A_i XOR A_j) & X) == 0. The bitwise AND of X and the XOR result must be zero. That means... |
>\n\nOkay, let's see. The problem is to calculate the probability that Chef gets A on the first toss and B on the second toss of an N-faced die. The die's faces have numbers written on them, which might not be distinct. So the probability is the product of the probability of getting A on the first toss and B on the sec... |
>\n\nOkay, let's tackle this problem. Hmm, the task is to find a minimal number of prefix swaps between two strings s and t such that one ends up all a's and the other all b's. So the goal is to split the a's into one string and the b's into the other. \n\nFirst, I need to think about the conditions required for a solu... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem statement carefully.\n\nSo the problem is about building a network of n nodes connected with the minimal number of wires (which is n-1 since it's a tree). Exactly k of these nodes are exit-nodes. Exit-nodes must have exactly one connection (deg... |
>\n\nOkay, let's see. I need to solve this programming problem. Let's read the problem carefully.\n\nThe problem is about assigning letters to keys on a keypad such that the total number of keystrokes is minimized. Each key can have a certain number of letters (given by keySize array), and each letter's frequency is gi... |
>\n\nOkay, let's see. I need to solve this problem where Alice and Bob are agents in Byteland, and I have to calculate the importance of each city based on their meeting points. Then sum up each city's importance multiplied by its number, modulo 1e9+7.\n\nHmm. So the problem says that for every pair of cities (A, B), t... |
>\n\nOkay, let's see. I need to find the last tree to catch fire when the fire spreads from K initial points. The fire spreads every minute to adjacent trees. Adjacent here probably means 4-directionally adjacent (up, down, left, right), or maybe 8-directional? Wait, the problem says that the distance to the nearest bu... |
>\n\nOkay, let's tackle this problem. Hmm. The problem is about Igor in a museum, and he can move around empty cells. The museum has walls between adjacent cells of different types (empty and impassable), and each such wall has a picture. We need to find, for several starting positions, the maximum number of pictures I... |
>\n\nOkay, let's tackle this problem step by step. The goal is to find the minimum number of moves required to make all elements in an array equal by dividing each element by any of its divisors in each move. Hmm, right. So each move allows us to divide an element by a divisor of its current value. And we need all elem... |
>\n\nOkay, I need to solve this programming problem. Let me read the problem carefully again.\n\nSo the problem is about Alice moving from one cell to another on a grid. The grid has land (0) and water (1). She can walk on land, but can't swim. So normally, if there's a path of land cells, she can reach. But if not, we... |
>\n\nOkay, let's try to tackle this problem. Hmm, the problem statement is a bit complex, so I need to parse it carefully.\n\nSo the task is to divide all n computers into k groups for each k from 1 to n, such that certain conditions are met. The main condition is about the difficulty values between pairs. Let's restat... |
>\n\nOkay, I need to solve this problem where for each node in a tree, I have to find the minimum XOR value between any two distinct nodes in its subtree. If the subtree has only one node (like a leaf), output -1. Let's think about how to approach this.\n\nFirst, the constraints are tight. T can be up to 1e5 and N up t... |
>\n\nOkay, I need to solve this programming problem. Let's read the problem carefully.\n\nSo, the problem is about finding the minimum maximum arrival time for both a train and a bus to reach town n, under the constraint that they can't be in the same town (except n) at the same time. The train moves only on railways, ... |
>\n\nOkay, let's see. I have to solve this problem where for each query, given a substring S[L..R], I need to count the number of substrings within that range which have at most K 0s and at most K 1s. Hmm.\n\nWait, the problem statement says that the substring S[i..j] must contain no character that occurs more than K t... |
>\n\nOkay, let's try to figure out how to solve this problem. So the problem is about moving disk heads such that all the required tracks are covered, and we need to find the minimum possible time required. Hmm.\n\nLet's start by understanding the problem statement again. We have n heads initially positioned at some tr... |
>\n\nOkay, let's tackle this problem. The goal is to find the sum of the line numbers of all possible permutations that match the given pattern (with 0s being unknown values). The sum needs to be modulo 1e9+7. \n\nFirst, let's understand the problem. Alice's favorite permutation has some zeros, which can be replaced by... |
>\n\nOkay, let's see. I need to solve this programming problem. Let's read the problem carefully.\n\nSo, Mahmoud wants to send a message. Each word in his message can be replaced with another word from the same group (same meaning), or left as is. The goal is to minimize the total cost of sending the message. The cost ... |
>\n\nOkay, let's see. I need to find the lex smallest string of length exactly k after performing delete and duplicate operations on the original string s. Hmm. The operations allowed are deleting the last character any number of times and duplicating the string (so s becomes s + s) any number of times. And I can do th... |
>\n\nOkay, let's see. I need to solve this programming problem. Let's read the problem carefully.\n\nSo, the task is about placing tiles on a 4x4 grid according to a given sequence of 0s and 1s. Each tile is either vertical (2x1) or horizontal (1x2). When a tile is placed, after placing it, any row or column that is fu... |
>\n\nOkay, let's try to understand this problem. So, Dasha needs to create a valid password by moving pointers on each of the n strings. The password must have at least one digit, one lowercase letter, and one of the symbols #, *, &. Each string corresponds to a character in the password, and the initial position of ea... |
>\n\nOkay, let's tackle this problem. So the task is to partition the numbers from 1 to N, excluding x, into two sets with equal sums. And we need to output the partition as a string where x is marked as '2' and others as '0' or '1'. If it's impossible, we print 'impossible'.\n\nFirst, I need to understand the conditio... |
>\n\nOkay, let's see. The problem is to handle multiple queries on an array, where each query is either an update or a count of non-decreasing subarrays in a certain range. Hmm, the challenge here is to handle these efficiently, especially since n and q can be up to 2e5. A naive approach would be way too slow.\n\nSo, f... |
>\n\nOkay, let's see. I need to determine whether Bob can move his king from his starting position to the target position without ever stepping into a square that's under check by Alice's queen. The king can move one step in any direction each turn. So, the problem is to check if there's a path from (b_x, b_y) to (c_x,... |
>\n\nOkay, let's see. I need to calculate the sum over all pairs i and j of the occurrences of s_i concatenated with s_j in the string t. Hmm. The straightforward approach would be for each pair (i,j), concatenate their strings and then count how many times that combined string appears in t. But given that n can be up ... |
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