You are given an integer array nums of length $n$ and an integer k.

The value of a contiguous subarray is defined as the difference between its maximum element and its minimum element.

You must select $k$ distinct subarrays of nums. Return the maximum possible sum of the values of the chosen subarrays.

Constraints:

• $1 \leq n ==$ nums.length $\leq 5 imes 10^4$

• $0 \leq$ nums[i] $\leq 10^9$

• $1 \leq k \leq \min(10^5, n imes (n + 1) / 2)$

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.