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question:Alice is a passionate gardener and she is setting up a new garden. She has a rectangular garden bed of dimensions n x m, which is initially empty (no plants). She has decided to plant different types of flowers in the garden bed. Each type of flower can cover a specific area of 1xk where k denotes the length of the flower bed. Alice wants to make sure that each row in her garden bed is completely filled with flowers so that there are no empty spots in any row. Given the dimensions of the garden bed and the length for each type of flower bed available, determine if Alice can fill the garden bed completely with the available flower beds. If it is possible, print "YES". Otherwise, print "NO". Input The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 50) — the dimensions of Alice's garden bed (number of rows and columns). The second line contains an integer k (1 ≤ k ≤ 50) — the length of each type of flower bed Alice has. Output Print "YES" if Alice can fill the garden bed completely using the flowers. Otherwise, print "NO". Examples Input 3 6 3 Output YES Input 4 7 2 Output NO Note In the first example, Alice can place two flower beds of length 3 in each row to fill the garden bed completely. In the second example, each row requires 7 units of length to be filled, but since the flower beds only have a length of 2, it cannot be filled completely with no empty spots.

answer:def can_fill_garden(n, m, k): Determines if the garden bed of dimensions n x m can be completely filled with flowers of length k. if m % k == 0: return "YES" else: return "NO"

question:Alice is a skilled chocolatier who creates special chocolate bars. One day, she decided to create chocolate bars in different shapes by breaking a large rectangular chocolate bar into smaller pieces. Each time she breaks a large bar, she makes a single straight cut that divides the bar into two smaller rectangles. She continues cutting until every piece is exactly a 1x1 square. Given the dimensions of the chocolate bar (width and height), determine the minimum number of cuts Alice needs to make to split the chocolate into 1x1 squares. Alice can make cuts either vertically or horizontally. Input The input consists of two integers width and height (1 ≤ width, height ≤ 106), representing the dimensions of the chocolate bar. Output Print a single integer: the minimum number of cuts needed to split the chocolate bar into 1x1 squares. Examples Input 2 3 Output 5 Input 4 4 Output 12 Input 5 7 Output 34 Note In the first example, Alice can make the following cuts: 1. First, she cuts vertically twice, resulting in three bars of size 1x3. 2. Then, she cuts each of the three bars horizontally twice, for a total of 6 pieces.

answer:def minimum_cuts(width, height): Calculate the minimum number of cuts needed to split the rectangular chocolate bar into 1x1 squares. Parameters: width (int): The width of the chocolate bar. height (int): The height of the chocolate bar. Returns: int: The minimum number of cuts. return width * height - 1

question:You are given a sequence of integers b1, b2, ..., bN. Find the length of the longest subsequence where the difference between consecutive elements is the same. Input The first line of input contains an integer T denoting the number of test cases. The description of T test cases follows. The first line of each test case contains an integer N. The second line of each test case contains N space-separated integers b1, b2, ..., bN respectively. Output For each test case, output a single line containing a single integer - the length of the longest subsequence with consecutive elements having the same difference. Constraints 1 ≤ T ≤ 10^4 1 ≤ N ≤ 10^5 -10^6 ≤ bi ≤ 10^6 Example Input: 1 7 1 2 3 4 1 2 3 Output: 4 Explanation The longest subsequence with a constant difference is [1, 2, 3, 4] and its length is 4.

answer:def longest_constant_difference_subsequence(T, cases): results = [] for case in cases: N, sequence = case if N == 1: results.append(1) continue max_len = 1 curr_len = 1 curr_diff = None for i in range(1, N): diff = sequence[i] - sequence[i-1] if diff == curr_diff: curr_len += 1 else: curr_diff = diff curr_len = 2 if curr_len > max_len: max_len = curr_len results.append(max_len) return results # Example input processing function def from_input_string(input_string: str): lines = input_string.strip().split("n") T = int(lines[0]) cases = [] idx = 1 for _ in range(T): N = int(lines[idx]) sequence = list(map(int, lines[idx + 1].split())) cases.append((N, sequence)) idx += 2 return T, cases # Example output processing function def to_output_string(output): return "n".join(map(str, output))

question:Given a matrix of integers where each cell contains either 0 or 1. A submatrix is a rectangular area of the matrix defined by selecting two rows and two columns. You need to determine the size of the largest square submatrix that contains only 1s. Constraints * 1 leq N, M leq 500 * The elements of the matrix are either 0 or 1. Input The first line contains two space-separated integers N and M, where N is the number of rows and M is the number of columns in the matrix. Each of the next N lines contains M space-separated integers (either 0 or 1), representing the elements of the matrix. Output Output a single integer, the size of the largest square submatrix that contains only 1s. Examples Input 3 4 1 1 0 1 1 1 1 1 1 1 1 0 Output 2 Input 2 2 1 0 0 1 Output 1

answer:def largestSquareSubmatrix(matrix): Finds the size of the largest square submatrix that contains only 1s. if not matrix or not matrix[0]: return 0 n = len(matrix) m = len(matrix[0]) dp = [[0] * m for _ in range(n)] max_square_len = 0 for i in range(n): for j in range(m): if matrix[i][j] == 1: dp[i][j] = 1 if i > 0 and j > 0: dp[i][j] += min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1]) max_square_len = max(max_square_len, dp[i][j]) return max_square_len