You are given an integer array nums and an integer k.

You need to partition nums into k contiguous non empty subarrays. The score of a subarray with sum $S$ is defined as $\frac{S \times (S + 1)}{2}$.

The total score of a partition is the sum of the scores of all its subarrays.

Return the minimum total score possible after partitioning nums into k subarrays.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 10^4$

• $1 \leq$ k $\leq$ nums.length

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.