<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 {
    unordered_map<int, bool> f;
    vector<int> l;

    bool dp(int state, int left) {
        if (left <= 0) return false;
        int m = (state << 9) | left;
        auto it = f.find(m);
        if (it != f.end()) return it->second;
        int s = state;
        while (s > 0) {
            int pow = s & -s;
            int d = l[pow];
            if (!dp(state - pow, left - d)) {
                f.emplace(m, true);
                return true;
            }
            s -= pow;
        }
        f.emplace(m, false);
        return false;
    }

public:
    bool canIWin(int maxChoosableInteger, int desiredTotal) {
        if (desiredTotal == 0) return true;
        if ((maxChoosableInteger + 1) * maxChoosableInteger / 2 < desiredTotal) return false;
        f.clear();
        l = vector<int>(1 << maxChoosableInteger, 0);
        for (int i = 0; i < maxChoosableInteger; ++i) l[1 << i] = i + 1;
        return dp((1 << maxChoosableInteger) - 1, desiredTotal);
    }
};
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