You are given a $0$ indexed $2 {D}$ integer matrix grid and an integer k.

Return the number of submatrices containing the top left cell grid[0][0] such that the sum of their elements is less than or equal to k.

Constraints:

• m == grid.length

• n == grid[i].length

• $1 \leq$ m, n $\leq 1000$

• $0 \leq$ grid[i][j] $\leq 1000$

• $1 \leq$ k $\leq 10^9$

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.