<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>



     #pragma GCCtarget("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma,tune=native")


class Solution {
public:
    int solve(  vector<vector<vector<int>>>&dp,int i,int f,int m,int& n,vector<int>&p)
    {
     
      if(i>=n)return 0;
      if(dp[i][f][m]!=-1)return dp[i][f][m];
      int st=0,re=f?-1:INT_MAX;
       for(int x=1;x<=min(2*m,n-i);x++)
       {
        st+=p[i+x-1];
        if(f)
        re=max(re,st+solve(dp,x+i,!f,max(m,x),n,p));
        else
        re=min(re,solve(dp,x+i,!f,max(m,x),n,p));
       }
       return dp[i][f][m]=re;
       
    }
    int stoneGameII(vector<int>& piles) {
        
     ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
        int n=piles.size();
        vector<vector<vector<int>>>dp(n+1,vector<vector<int>>(2,vector<int>(n+1,-1)));

        return solve(dp,0,1,1,n,piles);

        
    }
};
14331