<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:
        #这个可以 要用cache
        if sum(nums) % k != 0: return False
        target = sum(nums) // k
        nums.sort(reverse=True)

        @cache
        def dfs(subsets_found, current_sum, start_index, used):
            if subsets_found == k:
                return True

            if current_sum == target:
                return dfs(subsets_found + 1, 0, 0, tuple(used))
            
            used = list(used)
            for i in range(start_index, len(nums)):
                if nums[i] > target - current_sum or used[i]:
                    continue
                used[i] = True
                if dfs(subsets_found, current_sum + nums[i], i + 1, tuple(used)):
                    return True
                used[i] = False
            return False 

        return dfs(0, 0, 0, tuple([0 for _ in range(len(nums))]))
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