maximum-total-subarray-value-i

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

You need to choose exactly k non-empty subarrays nums[l..r] of nums. Subarrays may overlap, and the exact same subarray (same l and r) can be chosen more than once.

The value of a subarray nums[l..r] is defined as: max(nums[l..r]) - min(nums[l..r]).

The total value is the sum of the values of all chosen subarrays.

Return the maximum possible total value you can achieve.

Example 1:

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

Output: 4

Explanation:

One optimal approach is:

• Choose nums[0..1] = [1, 3]. The maximum is 3 and the minimum is 1, giving a value of 3 - 1 = 2.


• Choose nums[0..2] = [1, 3, 2]. The maximum is still 3 and the minimum is still 1, so the value is also 3 - 1 = 2.

Adding these gives 2 + 2 = 4.

Example 2:

Input: nums = [4,2,5,1], k = 3

Output: 12

Explanation:

One optimal approach is:

• Choose nums[0..3] = [4, 2, 5, 1]. The maximum is 5 and the minimum is 1, giving a value of 5 - 1 = 4.


• Choose nums[0..3] = [4, 2, 5, 1]. The maximum is 5 and the minimum is 1, so the value is also 4.


• Choose nums[2..3] = [5, 1]. The maximum is 5 and the minimum is 1, so the value is again 4.

Adding these gives 4 + 4 + 4 = 12.

Constraints:

• 1 <= n == nums.length <= 5 * 10​​​​​​​4


• 0 <= nums[i] <= 109


• 1 <= k <= 105