You are given a 2D integer array grid with size m x n. You are also given an integer k.
Your task is to calculate the number of paths you can take from the top-left cell (0, 0) to the bottom-right cell (m - 1, n - 1) satisfying the following constraints:
(i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j) if the target cell exists.XOR of all the numbers on the path must be equal to k.Return the total number of such paths.
\n\nSince the answer can be very large, return the result modulo 109 + 7.
\n
Example 1:
\n\nInput: grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11
\n\nOutput: 3
\n\nExplanation:
\n\nThe 3 paths are:
\n\n(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2)(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2)(0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)Example 2:
\n\nInput: grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2
\n\nOutput: 5
\n\nExplanation:
\n\nThe 5 paths are:
\n\n(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (2, 3)(0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → (2, 3)(0, 0) → (1, 0) → (1, 1) → (1, 2) → (1, 3) → (2, 3)(0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2) → (2, 3)(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (2, 3)Example 3:
\n\nInput: grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10
\n\nOutput: 0
\n\n
Constraints:
\n\n1 <= m == grid.length <= 3001 <= n == grid[r].length <= 3000 <= grid[r][c] < 160 <= k < 16给你一个大小为 m x n 的二维整数数组 grid 和一个整数 k 。
你的任务是统计满足以下 条件 且从左上格子 (0, 0) 出发到达右下格子 (m - 1, n - 1) 的路径数目：
(i, j) 走到格子 (i, j + 1) 或者格子 (i + 1, j) 。XOR 异或值必须 等于 k 。请你返回满足上述条件的路径总数。
\n\n由于答案可能很大，请你将答案对 109 + 7 取余 后返回。
\n\n
示例 1：
\n\n输入：grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11
\n\n输出：3
\n\n解释：
\n\n3 条路径分别为：
\n\n(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2)(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2)(0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)示例 2：
\n\n输入：grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2
\n\n输出：5
\n\n解释：
\n\n5 条路径分别为：
\n\n(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (2, 3)(0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → (2, 3)(0, 0) → (1, 0) → (1, 1) → (1, 2) → (1, 3) → (2, 3)(0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2) → (2, 3)(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (2, 3)示例 3：
\n\n输入：grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10
\n\n输出：0
\n\n\n
提示：
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