<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>

from functools import cache
class Solution:
    def canPartitionKSubsets(self, nums: List[int], k: int) -> bool:
        n = len(nums)
        nsum = sum(nums)
        ssize = nsum//k
        filled = 2**n - 1
        if nsum%k:
            return False
        
        @cache
        def dp(csum,bmask,cseg):
            if cseg == k and bmask == filled:
                return True
            for i,num in enumerate(nums):
                if (bmask & (1 << i) == 0) and csum+num <= ssize:
                    nseg = cseg+int(csum+num == ssize)
                    nsum = csum+num if csum+num < ssize else 0
                    nmask = bmask | (1 << i)
                    if dp(nsum,nmask, nseg):
                        return True
            return False
        return dp(0, 0, 0)
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