You are given an n $\times$ m 2D integer matrix grid, an integer array limits of length n, and an integer k.

Your task is to select at most k elements from grid such that the number of elements chosen from row i does not exceed limits[i].

Return the maximum possible sum of the chosen elements.

Constraints:

• n $==$ grid.length $==$ limits.length

• m $==$ grid[i].length

• $1 \leq$ n, m $\leq 500$

• $0 \leq$ grid[i][j] $\leq 10^5$

• $0 \leq$ limits[i] $\leq$ m

• $0 \leq$ k $\leq \min($n $\times$ m, sum(limits) $)$

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.