Determine winner in optimal-play card game

Given a row of N cards with integer values (values may be positive, zero, or negative), two players alternately pick either the leftmost or rightmost card. Both play optimally to maximize their total sum. Implement a function winner_score(cards: List[int]) -> int that returns the maximum score difference (first − second). Then:

• Explain your time and space complexity.
• Modify the function to also return one optimal sequence of picks (as a list of indices). Constraints: 1 ≤ N ≤ 2000.