<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 {
    int* dp;
    int currentMask;
    int mct;
    bool recursion(int target){
        // This function will return true, if with the given target and unused numbers, can the player win? if the caller of this function gets false means the opponent cannot with with this combination. if the caller gets true, means this combination can make the opponent win.
        if(target <= 0){
            // Target is already met so the caller to this target won.
            return false;
        }
        if(dp[currentMask] != -1){
            return dp[currentMask];
        }
        for(int i = 0; i < mct; i++){
            if(!(currentMask&(1<<i))){
                currentMask |= (1<<i);
                bool didOpponentWon = recursion(target - i - 1);
                currentMask &= (~(1<<i));
                if(!didOpponentWon){
                    dp[currentMask] = 1;
                    return true;
                }
            }
        }
        return (dp[currentMask] = 0);
    }
public:
    bool canIWin(int mct, int dt) {
        this->mct = mct;
        if(dt < 2){
            return true;
        }
        if(mct*(mct+1)/2 < dt){
            return false;
        }
        if(mct*(mct+1)/2 == dt){
            return mct%2;
        }
        dp = new int[1<<mct];
        memset(dp, -1, (1<<mct) * sizeof(int));
        return recursion(dt);
    }
};
34937