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

An island is formed by connected cells with values strictly greater than $0$, where connectivity is defined horizontally or vertically. You may assume all four edges of the grid are surrounded by $0$.

The total value of an island is the sum of all cell values belonging to that island.

Return the total number of islands whose total value is divisible by k.

Constraints:

• m $==$ grid.length

• n $==$ grid[i].length

• $1 \leq$ m, n $\leq 1000$

• $1 \leq$ m * n $\leq 10^5$

• $0 \leq$ grid[i][j] $\leq 10^6$

• $1 \leq$ k $\leq 10^6$

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.