Given an integer array nums and an integer k, split nums into k non-empty subarrays such that the largest sum of any subarray is minimized. Return the minimized largest sum of the split. A subarray is a contiguous part of the array.

• An array nums.
• An integer k.

Input: nums = [7, 2, 5, 10, 8], k = 2
Output: 18
Explanation: Split into [7, 2, 5] and [10, 8]. Max sum is max(14, 18) = 18.

• Other splits like [7, 2] and [5, 10, 8] would have max sum 23.