Maximum Sum Subarray from Ends

Early February, 2026

You are given an array of integers nums and an integer k. You must pick exactly k elements from the array. At each step, you may pick only from the front or the back of the array. However, you cannot skip elements: To pick an element at index i from the front, all elements before it must already be picked. To pick an element at index j from the back, all elements after it must already be picked. Goal: Return the maximum possible sum of the k selected elements. Example nums = [1, 8, 2, 0, 9, 3] k = 3 Ans = 13 Possible selections: Pick all 3 from the front: 1 + 8 + 2 = 11 Pick 2 from the front, 1 from the back: 1 + 8 + 3 = 12 Pick 1 from the front, 2 from the back: 1 + 3 + 9 = 13 Pick all 3 from the back: 3 + 9 + 0 = 12