![](\"https://assets.leetcode.com/uploads/2022/08/13/image-20220813183124-1.png\")
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.
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Example 1:
\n\n\nInput: grid = [[5,2,4],[3,0,5],[0,7,2]], k = 3\nOutput: 2\nExplanation: There are two paths where the sum of the elements on the path is divisible by k.\nThe first path highlighted in red has a sum of 5 + 2 + 4 + 5 + 2 = 18 which is divisible by 3.\nThe second path highlighted in blue has a sum of 5 + 3 + 0 + 5 + 2 = 15 which is divisible by 3.\n\n\n
Example 2:
\n![](\"https://assets.leetcode.com/uploads/2022/08/17/image-20220817112930-3.png\")
\n\nInput: grid = [[0,0]], k = 5\nOutput: 1\nExplanation: The path highlighted in red has a sum of 0 + 0 = 0 which is divisible by 5.\n\n\n
Example 3:
\n![](\"https://assets.leetcode.com/uploads/2022/08/12/image-20220812224605-3.png\")
\n\nInput: grid = [[7,3,4,9],[2,3,6,2],[2,3,7,0]], k = 1\nOutput: 10\nExplanation: Every integer is divisible by 1 so the sum of the elements on every possible path is divisible by k.\n\n\n
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Constraints:
\n\nm == grid.lengthn == grid[i].length1 <= m, n <= 5 * 1041 <= m * n <= 5 * 1040 <= grid[i][j] <= 1001 <= k <= 50给你一个下标从 0 开始的 m x n 整数矩阵 grid 和一个整数 k 。你从起点 (0, 0) 出发，每一步只能往 下 或者往 右 ，你想要到达终点 (m - 1, n - 1) 。
请你返回路径和能被 k 整除的路径数目，由于答案可能很大，返回答案对 109 + 7 取余 的结果。
\n\n
示例 1：
\n\n
输入：grid = [[5,2,4],[3,0,5],[0,7,2]], k = 3\n输出：2\n解释：有两条路径满足路径上元素的和能被 k 整除。\n第一条路径为上图中用红色标注的路径，和为 5 + 2 + 4 + 5 + 2 = 18 ，能被 3 整除。\n第二条路径为上图中用蓝色标注的路径，和为 5 + 3 + 0 + 5 + 2 = 15 ，能被 3 整除。\n\n\n
示例 2：
\n\n输入：grid = [[0,0]], k = 5\n输出：1\n解释：红色标注的路径和为 0 + 0 = 0 ，能被 5 整除。\n\n\n
示例 3：
\n\n输入：grid = [[7,3,4,9],[2,3,6,2],[2,3,7,0]], k = 1\n输出：10\n解释：每个数字都能被 1 整除，所以每一条路径的和都能被 k 整除。\n\n\n
\n\n
提示：
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