Partition k groups squared cost

Partition an array of non-negative integers into exactly k contiguous groups to minimize the total cost, where the cost of a group is (sum of its elements) squared. Return the minimum total cost. Constraints: 1 <= k <= length <= 2000, 0 <= each element <= 1000. The cost function is convex/monotone so the layered DP admits divide-and-conquer optimization, but a correct O(k*n^2) reference is acceptable for the bounds.