<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:
        total_sum = sum(nums)
        if total_sum % k:
            return False
        one_partition_sum = total_sum // k
        is_possible = [False] * (1 << len(nums))
        valid_masks = []
        mask_sum = [0] * (1 << len(nums))
        for mask in range(1, 1 << len(nums)):
            current_sum = 0
            for i in range(len(nums)):
                if mask & (1 << i):
                    current_sum += nums[i]
            if current_sum == one_partition_sum:
                valid_masks.append(mask)
            mask_sum[mask] = current_sum
            is_possible[mask] = current_sum == one_partition_sum
        for current_partition in range(1, k):
            for current_mask in range(1, (1 << len(nums))):
                if is_possible[current_mask]:
                    for mask in valid_masks:
                        if not (mask & current_mask):
                            is_possible[mask | current_mask] = True
        return is_possible[(1 << len(nums)) - 1]
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