<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:
        mask = 0
        seen = {}

        if not nums:
            return False

        n = len(nums)
        target_sum = sum(nums)

        if target_sum % k != 0:
            return False

        target = target_sum // k

        count = 0

        def backtrack(curr_sum, count, index):
            nonlocal mask
            if count == k-1:
                return True
            
            if curr_sum > target:
                return False

            if mask in seen:
                return seen[mask]

            if curr_sum == target:
                seen[mask] = backtrack(0, count+1, 0)
                return seen[mask]

            for i in range(index, n):
                if (mask>>i) & 1 == 0:
                    mask = mask | (1 << i)
                    res = backtrack(curr_sum + nums[i], count, i+1)
                    if res:
                        seen[mask] = res
                        return seen[mask]
                    mask = mask ^ (1<<i)
            seen[mask] = False
            return seen[mask]
        
        return backtrack(0, 0, 0)
        

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