Split Array Largest Sum - Painter's Partition

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. ### Constraints - `1 <= nums.length <= 1000` - `0 <= nums[i] <= 10^6` - `1 <= k <= min(50, nums.length)` ### Input Format First line contains the integer `k`. Second line contains space-separated integers representing `nums`. ### Output Format Print the minimized largest subarray sum.