<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:
    def canIWin(self, maxChoosableInteger, desiredTotal):
        """
        :type maxChoosableInteger: int
        :type desiredTotal: int
        :rtype: bool
        """
        if desiredTotal <= 0:
            return True
        s = maxChoosableInteger*(maxChoosableInteger+1)
        if s < 2*desiredTotal:
            return False
        if s == 2*desiredTotal:
            if maxChoosableInteger % 2 == 1:
                return True
            else:
                return False
        seen = {}
        def can_win(x,y):
            
            temp = False
            readyset = set(x)
            for i in readyset:
                if i >= y:
                    return True
                else:
                    readyset.remove(i)
                    cur = frozenset(readyset)
                    tup = (cur, y-i)
                    if tup in seen:
                        if not seen[tup]:
                            
                            return True
                    else:
                        ans = can_win(cur, y-i)
                        seen[tup] = ans
                        if not ans:
                            return True
                    readyset.add(i)
            #print(x,y,temp)
            return temp

        return can_win(frozenset(range(1,1 + maxChoosableInteger)), desiredTotal)

        
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