<p>In the &quot;100 game&quot; two players take turns adding, to a running total, any integer from <code>1</code> to <code>10</code>. The player who first causes the running total to <strong>reach or exceed</strong> 100 wins.</p>

<p>What if we change the game so that players <strong>cannot</strong> re-use integers?</p>

<p>For example, two players might take turns drawing from a common pool of numbers from 1 to 15 without replacement until they reach a total &gt;= 100.</p>

<p>Given two integers <code>maxChoosableInteger</code> and <code>desiredTotal</code>, return <code>true</code> if the first player to move can force a win, otherwise, return <code>false</code>. Assume both players play <strong>optimally</strong>.</p>

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

<pre>
<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 11
<strong>Output:</strong> false
<strong>Explanation:</strong>
No matter which integer the first player choose, the first player will lose.
The first player can choose an integer from 1 up to 10.
If the first player choose 1, the second player can only choose integers from 2 up to 10.
The second player will win by choosing 10 and get a total = 11, which is &gt;= desiredTotal.
Same with other integers chosen by the first player, the second player will always win.
</pre>

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

<pre>
<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 0
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 1
<strong>Output:</strong> true
</pre>

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

<ul>
	<li><code>1 &lt;= maxChoosableInteger &lt;= 20</code></li>
	<li><code>0 &lt;= desiredTotal &lt;= 300</code></li>
</ul>

class Solution {
public:

    int func(int tar,int maxi,int score,int fl,int num,vector<int>& dp){

        if(score>=tar){
            return 0;
        }

        if(dp[num]!=-1) return dp[num];

       
            for(int i=0;i<maxi;i++){
                int temp=num;
                if((temp & (1<<i)) == 0){
                    temp|=(1<<i);
                    int ans=func(tar,maxi,score+i+1,1,temp,dp);
                    if(!ans) return dp[num]=1;
                }
            }
            return dp[num]=0;
        
        
    }

    bool canIWin(int maxi, int tar) {
          int sum=0;
          if(tar>((maxi*maxi+maxi)/2) )return false;
          if(tar<=maxi)return true;
          vector<int> dp(pow(2,20)+1,-1);
          return func(tar,maxi,0,0,0,dp);
    }
};
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