<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 solve(int a,int b,int sum,bool alice,int &visited,map<pair<int,bool>,int> &dp){
        if(dp.find({visited,alice}) != dp.end()) return dp[{visited,alice}];

        if(alice){
            int maxAvailable = 0;
            for(int i=0;i<a;i++){
                if(((visited>>i)&1) == 0) maxAvailable = max(maxAvailable,i+1);
            }
            if(maxAvailable+sum >= b) return dp[{visited,alice}] = true;

            bool ans = false;
            for(int i=a-1;i>=0;i--){
                if( ((visited>>i)&1) == 0 ){
                    int temp = visited;
                    visited = visited | (1 << i);
                    // cout<<i+1<<" "<<alice<<endl;
                    bool tempans = solve(a,b,sum+i+1,!alice,visited,dp);
                    visited = temp;

                    if(tempans == false) {ans= true;break;}
                }
            }
            return dp[{visited,alice}] = ans;
        }
        else {
            int maxAvailable = 0;
            for(int i=a-1;i>=0;i--){
                if(((visited>>i)&1) == 0) maxAvailable = max(maxAvailable,i+1);
            }
            if(maxAvailable+sum >= b) return dp[{visited,alice}] = true;
            bool ans = false;
            for(int i=0;i<a;i++){
                if( ((visited>>i)&1) == 0 ){
                    int temp = visited;
                    visited = visited | (1 << i);
                    bool tempans = solve(a,b,sum+i+1,!alice,visited,dp);
                    visited = temp;
                    // if(tempans == true) {ans= false;break;}
                    if(tempans == false) {ans = true;break;}
                }
            }

            return dp[{visited,alice}] = ans;
        }
    }
    bool canIWin(int maxChoosableInteger, int desiredTotal) {
        // if(maxChoosableInteger >= desiredTotal) return true;
        int totalweget = (maxChoosableInteger * (maxChoosableInteger+1))/2;
        if(totalweget < desiredTotal) return false;
        map<pair<int,bool>,int> dp;
        int visited = 0;
        return solve(maxChoosableInteger,desiredTotal,0,true,visited,dp);
        
    }
};
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