{leetcode}/problems/paths-in-matrix-whose-sum-is-divisible-by-k/[LeetCode - 2435. Paths in Matrix Whose Sum Is Divisible by K ^]
You are given a 0-indexed m x n integer matrix grid and an integer k. You are currently at position (0, 0) and you want to reach position (m - 1, n - 1) moving only down or right.
Return_ the number of paths where the sum of the elements on the path is divisible by _`k`. Since the answer may be very large, return it modulo 109 + 7.
Example 1: <img src="https://assets.leetcode.com/uploads/2022/08/13/image-20220813183124-1.png" style="width: 437px; height: 200px;" />
Input: grid = [[5,2,4],[3,0,5],[0,7,2]], k = 3 Output: 2 Explanation: There are two paths where the sum of the elements on the path is divisible by k. The first path highlighted in red has a sum of 5 + 2 + 4 + 5 + 2 = 18 which is divisible by 3. The second path highlighted in blue has a sum of 5 + 3 + 0 + 5 + 2 = 15 which is divisible by 3.
Example 2: <img src="https://assets.leetcode.com/uploads/2022/08/17/image-20220817112930-3.png" style="height: 85px; width: 132px;" />
Input: grid = [[0,0]], k = 5 Output: 1 Explanation: The path highlighted in red has a sum of 0 + 0 = 0 which is divisible by 5.
Example 3: <img src="https://assets.leetcode.com/uploads/2022/08/12/image-20220812224605-3.png" style="width: 257px; height: 200px;" />
Input: grid = [[7,3,4,9],[2,3,6,2],[2,3,7,0]], k = 1 Output: 10 Explanation: Every integer is divisible by 1 so the sum of the elements on every possible path is divisible by k.
Constraints:
-
m == grid.length -
n == grid[i].length -
1 ⇐ m, n ⇐ 5 * 104 -
1 ⇐ m * n ⇐ 5 * 104 -
0 ⇐ grid[i][j] ⇐ 100 -
1 ⇐ k ⇐ 50