<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 __init__(self):
        self.nums = []
        self.target_sum = 0
        self.target_count = 0
        self.found = False
    
    @functools.lru_cache(None)
    def explore(self, count: int, curr_sum: int, mask: int) -> None:
        if count == self.target_count:
            self.found = True
            return
        
        if self.found:
            return
        
        for i in range(len(self.nums)):
            state = 1 << i
            if state & mask or curr_sum + self.nums[i] > self.target_sum:
                continue

            nmask = mask | state
            if curr_sum + self.nums[i] < self.target_sum:
                self.explore(count, curr_sum + self.nums[i], nmask)
            elif curr_sum + self.nums[i] == self.target_sum:
                self.explore(count + 1, 0, nmask)

    def canPartitionKSubsets(self, nums: List[int], k: int) -> bool:
        if sum(nums) % k != 0:
            return False
        
        self.nums = sorted(nums, reverse=True)
        self.target_sum = sum(nums) // k
        self.target_count = k
        
        self.explore(0, 0, 0)

        return self.found
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