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410\. Split Array Largest Sum

Hard

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.

**Example 1:**

**Input:** nums = [7,2,5,10,8], k = 2

**Output:** 18

**Explanation:** There are four ways to split nums into two subarrays. The best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.

**Example 2:**

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

**Output:** 9

**Explanation:** There are four ways to split nums into two subarrays. The best way is to split it into [1,2,3] and [4,5], where the largest sum among the two subarrays is only 9.

**Constraints:**

*   `1 <= nums.length <= 1000`
*   0 <= nums[i] <= 106
*   `1 <= k <= min(50, nums.length)`




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