<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <code>true</code> if it is possible to divide this array into <code>k</code> non-empty subsets whose sums are all equal.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [4,3,2,3,5,2,1], k = 4
<strong>Output:</strong> true
<strong>Explanation:</strong> It is possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4], k = 3
<strong>Output:</strong> false
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 16</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
	<li>The frequency of each element is in the range <code>[1, 4]</code>.</li>
</ul>

class Solution:
    def canPartitionKSubsets(self, nums: List[int], k: int) -> bool:
        if sum(nums)%k: return False
        S = sum(nums)//k
        n = len(nums)
        s = [0]*(1<<n)
        for i in range(n):
            bit = 1<<i
            for j in range(bit):
                s[j|bit]=s[j]+nums[i]
        keys = set()
        for i in range(1<<n):
            if s[i]==S: keys.add(i)
        @cache
        def dfs(mask):
            if mask==0: return True
            res = False
            for g in keys:
                if g|mask==mask:
                    res|=dfs(mask^g)
            return res
        return dfs((1<<n)-1)

        
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