You are given an integer array nums and two integers k and m.

Find the maximum possible sum of k disjoint subarrays of nums such that each chosen subarray has a length of at least m.

Return this maximum sum.

Constraints:

• $1 \leq$ nums.length $\leq 2000$

• $-10^4 \leq$ nums[i] $\leq 10^4$

• $1 \leq$ k $\leq \lfloor$nums.length $/$ m$\rfloor$

• $1 \leq$ m $\leq 3$

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.