<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:
    bool helper_win(int m, int n, int bitsnum, vector<int>& dp){
        // if(n <= 0){
        //     dp[bitsnum] = 1;
        //     return true;
        // }
        if(dp[bitsnum] != -1){
            return (dp[bitsnum] == 0) ? false: true;
        }
        for(int i = m; i >= 1; i--){
            if(((1 << (i-1)) & bitsnum) == 0){
                if(n-i <= 0){
                    dp[bitsnum] = 1;
                    return true;
                }
                if(!helper_win(m, n-i, bitsnum | (1 << (i-1)), dp)){
                    dp[bitsnum] = 1;
                    return true;
                }
            }
        }
        return false;
    }
    bool canIWin(int maxChoosableInteger, int desiredTotal) {
        int m = maxChoosableInteger, n = desiredTotal;
        if(m >= n){
            return true;
        }
        if(m*(m+1)/2 < n){
            return false;
        }
        if(m*(m+1)/2 == n){
            return (m%2 == 1);
        }
        int size = 1 << m;
        vector<int> dp(size, -1);
        return helper_win(m, n, 0, dp);
    }
};
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