Alex and Lee continue their games with piles of stones. There are a number of piles arranged
in a row, and each pile has a positive integer number of
stones piles[i]. The objective of the game is to end with the most stones.
Alex and Lee take turns, with Alex starting first. Initially, M = 1.
On each player's turn, that player can take all the stones in the
first X remaining piles, where 1 <= X <= 2M.
Then, we set M = max(M, X).
The game continues until all the stones have been taken.
Assuming Alex and Lee play optimally, return the maximum number of stones Alex can get.
Example 1:
Input: piles = [2,7,9,4,4] Output: 10 Explanation: If Alex takes one pile at the beginning, Lee takes two piles, then Alex takes 2 piles again. Alex can get 2 + 4 + 4 = 10 piles in total. If Alex takes two piles at the beginning, then Lee can take all three piles left. In this case, Alex get 2 + 7 = 9 piles in total. So we return 10 since it's larger.
Constraints:
1 <= piles.length <= 1001 <= piles[i] <= 10 ^ 4