<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:
        n = len(nums)
        total_sum = sum(nums)
        target_sum = total_sum // k
        if total_sum % k != 0:
            return False

        self.memo = {}

        def dfs(subset_sum, k):
            if k == 0:
                return True
            if subset_sum == target_sum:
                return dfs(0, k-1)

            key = tuple(used)
            if key in self.memo:
                return self.memo[key]

            for i in range(n):
                if used[i]:
                    continue
                if subset_sum + nums[i] > target_sum:
                    break
                used[i] = True
                if dfs(subset_sum+nums[i], k):
                    key = tuple(used)
                    self.memo[key] = True
                    return True
                used[i]= False

            key = tuple(used)
            self.memo[key] = False

        used = [False for _ in range(n)]
        nums.sort(reverse=True)
        return dfs(0, k)
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