<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:
        target = sum(nums) // k
        if(sum(nums) % k != 0 or len(nums) < k or max(nums) > target):
            return False

        nums.sort(reverse=True)
        used = [False] * len(nums)

        memo = {}

        def dfs(completed, curr_sum):
            if "".join(map(lambda x: str(x), used)) in memo:
                return memo["".join(map(lambda x: str(x), used))]

            if completed == k:
                return True
            
            if curr_sum > target:
                print("hi")
                memo["".join(map(lambda x: str(x), used))] = False
                return False
            
            if curr_sum == target:
                memoiz = dfs(completed + 1, 0)
                memo["".join(map(lambda x: str(x), used))] = memoiz

                return dfs(completed + 1, 0)

            for i in range(len(nums)):
                if used[i] or nums[i] + curr_sum > target:
                    continue
                used[i] = True
                ret = dfs(completed, curr_sum + nums[i])
                if ret:
                    return True
                else: 
                    memo["".join(map(lambda x: str(x), used))] = ret
                used[i] = False
            
            memo["".join(map(lambda x: str(x), used))] = False
            return False

        return dfs(0, 0)
                

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