<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:

        if sum(nums) % k:
            return False

        nums.sort(reverse=True)
        target = sum(nums) // k
        visited = [False] * len(nums)

        if nums[0] > target:
            return False
        
        memo = {}
        def backtrack(start_idx, subset_sum, subset_cnt) -> bool:

            if tuple(visited) in memo:
                return memo[tuple(visited)]
            if subset_cnt == k:
                memo[tuple(visited)] = True
                return True

            if target == subset_sum:
                return backtrack(0, 0, subset_cnt+1)

            
            for idx in range(start_idx, len(nums)):
                num = nums[idx]
                if visited[idx] or subset_sum + nums[idx] > target:
                    continue
                visited[idx] = True
                if backtrack(idx+1, subset_sum + nums[idx], subset_cnt):
                    return True
                visited[idx] = False
            memo[tuple(visited)] = False
            return False

        
        return backtrack(0, 0, 0)
        
36425