<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 mx;
int total;
unordered_map<string,bool> mp;

bool rec(int x,int p)
{
    if(total<=0) return true;

    string key=to_string(x)+" "+to_string(p);

    if(mp.find(key)!=mp.end()) return mp[key];

    bool ok=false;

    for(int i=1;i<=mx;i++)
    {
        if(ok) break;
        if((x&(1<<i))==0)
        {
            

            if(total-i<=0)
            {
                ok=true;
            }
            else
            {
                total-=i;
                ok|=!(rec((x|(1<<i)),p^1));
                total+=i;
            }

            // x=x^(1<<i);
        }
    }
    return mp[key]=ok;
}

    bool canIWin(int mxc, int totall) {
        mx=mxc;
        mp.clear();
        total=totall;
        int x=pow(2,mxc+1);
        if((mxc+1)*mxc<(2*total)) return false;
        return rec(x,0);
    }
};
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