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.
Since the answer can be very large, return the result modulo 109 + 7.
Example 1:
Input: grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11
Output: 3
Explanation:
The 3 paths are:
(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:
Input: grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2
Output: 5
Explanation:
The 5 paths are:
(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:
Input: grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10
Output: 0
Constraints:
1 <= m == grid.length <= 3001 <= n == grid[r].length <= 3000 <= grid[r][c] < 160 <= k < 16