You are given an m $ imes$ n integer matrix grid and an integer k.

You start at the top left cell $(0, 0)$ and want to reach the bottom right cell (m $- 1$, n $- 1$). From any cell, you can only move either down or right.

The XOR value of a path is the bitwise XOR sum of all elements along that path.

Return the total number of paths from $(0, 0)$ to (m $- 1$, n $- 1$) whose XOR value equals k. Since the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ m $==$ grid.length $\leq 300$

• $1 \leq$ n $==$ grid[r].length $\leq 300$

• $0 \leq$ grid[r][c] $< 16$

• $0 \leq$ k $< 16$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.