<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 != 0:
            return False

        target = sum(nums) // k
        n = len(nums)

        memo = {}

        def dfs(cur_target, status, idx):
            if cur_target == 0 and status == "1" * n:
                return True

            if cur_target < 0:
                return False

            if (cur_target, status) in memo:
                return memo[(cur_target, status)]

            if cur_target == 0:
                cur_target = target
                idx = 0

            for i in range(idx, n):
                if status[i] == "0":
                    res = dfs(cur_target - nums[i], status[:i] + "1" + status[i+1:], i + 1)
                    if res:
                        return True

            memo[(cur_target, status)] = False
            return False

        return dfs(target, "0" * n, 0)

            
            

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