Given an integer list nums and an integer k, split nums into k non-empty subarrays such that the largest sum among these subarrays is minimized. The task is to find the minimized largest sum by choosing the split such that the largest sum of every split of subarrays is the minimum among the sum of other splits.

Constraints:

• $1\leq$ nums.length $\leq 10^3$

• $0\leq$ nums[i] $\leq 10^4$

• $1\leq$ k $\leq$ nums.length