Maximum Strength of K Disjoint Subarrays

You are given an array of integers nums with length n, and a positive odd integer k.

Select exactly k disjoint subarrays sub1, sub2, ..., subk from nums such that the last element of subi appears before the first element of sub{i+1} for all 1 <= i <= k - 1. The goal is to maximize their combined strength.

The strength of the selected subarrays is defined as:

strength = k * sum(sub1) - (k - 1) * sum(sub2) + (k - 2) * sum(sub3) - ... - 2 * sum(sub{k-1}) + sum(subk)

where sum(subi) is the sum of the elements in the i-th subarray.

Return the maximum possible strength that can be obtained from selecting exactly k disjoint subarrays from nums.

Note that the chosen subarrays don't need to cover the entire array.