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.

Example 1:

Input: nums = [1,2,3,-1,2], k = 3

Output: 22

Explanation:

The best possible way to select 3 subarrays is: nums[0..2], nums[3..3], and nums[4..4]. The strength is calculated as follows:

strength = 3 * (1 + 2 + 3) - 2 * (-1) + 2 = 22

Example 2:

Input: nums = [12,-2,-2,-2,-2], k = 5

Output: 64

Explanation:

The only possible way to select 5 disjoint subarrays is: nums[0..0], nums[1..1], nums[2..2], nums[3..3], and nums[4..4]. The strength is calculated as follows:

strength = 5 * 12 - 4 * (-2) + 3 * (-2) - 2 * (-2) + (-2) = 64

Example 3:

Input: nums = [-1,-2,-3], k = 1

Output: -1

Explanation:

The best possible way to select 1 subarray is: nums[0..0]. The strength is -1.

Constraints:

• 1 <= n <= 104
• -109 <= nums[i] <= 109
• 1 <= k <= n
• 1 <= n * k <= 106
• k is odd.