Alice and Bob are playing a game with piles of stones arranged in a row, where the number of stones in each pile is given by the integer array piles.

Alice begins the game. At the start, the value of M is set to $1$.

On each turn, a player can take all the stones from the first X remaining piles, where $1 \leq X \leq 2M$. Following this move, the value of M is updated to $\max(M, X)$.

The game continues until all piles have been taken. Assuming both Alice and Bob play optimally to maximize their total number of stones, return the maximum number of stones Alice can obtain.

Constraints:

• $1 \leq$ piles.length $\leq 100$

• $1 \leq$ piles[i] $\leq 10^4$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.