<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 {
private:
    // vector<vector<int>> dp;
    vector<int> dp;

    int n, x;
    
    int rec( int lvl, int bitmask ){

        if( lvl <= 0 )
            return false;
        
        // cout<<lvl<<","<<dp[bitmask] <<" ";

        if( dp[bitmask] != -1 ){
            return dp[bitmask] ;
        }
        
        for(int i=1; i <= x;i++){

            if( bitmask&(1<<i) )
                continue;

            if( !rec(lvl - i, bitmask|(1<<i) ) )
                return dp[bitmask] = 1;
            
        }
        return dp[bitmask] = 0;
    }
public:
    bool canIWin(int maxChoosableInteger, int desiredTotal) {
        
        x = maxChoosableInteger;
        n = desiredTotal;

        if( n <= x )
            return true;
        
        if( (x*(x+1))/2 < n )
            return false;

        // dp.assign(n+1, vector<int>( (1<<(x+1)), -1 ) );
        dp.assign(1<<(x+1), -1 ) ;

        return rec(n, 0);
    }
};
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