<p>Alice and Bob continue their games with piles of stones. There are a number of piles <strong>arranged in a row</strong>, and each pile has a positive integer number of stones <code>piles[i]</code>. The objective of the game is to end with the most stones.</p>

<p>Alice and Bob take turns, with Alice starting first.</p>

<p>On each player&#39;s turn, that player can take <strong>all the stones</strong> in the <strong>first</strong> <code>X</code> remaining piles, where <code>1 &lt;= X &lt;= 2M</code>. Then, we set <code>M = max(M, X)</code>. Initially, M = 1.</p>

<p>The game continues until all the stones have been taken.</p>

<p>Assuming Alice and Bob play optimally, return the maximum number of stones Alice can get.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">piles = [2,7,9,4,4]</span></p>

<p><strong>Output:</strong> <span class="example-io">10</span></p>

<p><strong>Explanation:</strong></p>

<ul>
	<li>If Alice takes one pile at the beginning, Bob takes two piles, then Alice takes 2 piles again. Alice can get <code>2 + 4 + 4 = 10</code> stones in total.</li>
	<li>If Alice takes two piles at the beginning, then Bob can take all three piles left. In this case, Alice get <code>2 + 7 = 9</code> stones in total.</li>
</ul>

<p>So we return 10 since it&#39;s larger.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">piles = [1,2,3,4,5,100]</span></p>

<p><strong>Output:</strong> <span class="example-io">104</span></p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= piles.length &lt;= 100</code></li>
	<li><code>1 &lt;= piles[i]&nbsp;&lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int sol(vector<int>&a, int ind, int m, int alice, vector<vector<vector<int>>>&dp){
        if(ind>=a.size())return 0;

        if(dp[ind][m][alice]!=-1){
            return dp[ind][m][alice];
        }

        int rtA = 0, rtB = INT_MAX;
        int sm = 0, count = 0;

        for(int i=ind;i<ind+(2*m) && i<a.size();i++){
            count++;
            sm += a[i];
            // cout<<i;
            if(alice){
                rtA = max(rtA,sm + sol(a,i+1,max(m,count),1-alice,dp));
            }else{
                rtB = min(rtB,sol(a,i+1,max(m,count),1-alice,dp));
            }
        }
        // cout<<endl;
        if(alice)return dp[ind][m][alice] = rtA;
        return dp[ind][m][alice] = rtB;
    }
    int stoneGameII(vector<int>& piles) {
        int m=1;
        int n = piles.size();
        int mm = 50;
        vector<vector<vector<int>>>dp(n, vector<vector<int>>(mm,vector<int>(2,-1)));
        return sol(piles, 0, m, 1, dp);
    }
};
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