<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:
        size = len(nums)
        total_sum = sum(nums)
        if total_sum % k != 0:
            return False
        
        self.subset_sum = total_sum / k
        self.k = k

        mask = 0
        self.memo = {}
        ans = self.recursive(nums, 0, 0, mask)
        # print(self.memo)
        return ans




    def recursive(self, nums, curr_sum, count, mask):
        if count == self.k - 1:
            return True
        
        if curr_sum > self.subset_sum :
            return False
        
        if curr_sum == self.subset_sum:
            return self.recursive(nums, 0, count + 1, mask)
    
        if mask == (1 << len(nums) - 1):
            return False
        
        key = (mask)
        if key not in self.memo:
            # if key == (0, 0):
            #     print(key)
            #     print(self.memo)
            res = False
            for index in range(len(nums)):
                if not mask & 1 << index:
                    mask ^= 1 << index
                    res = res or (self.recursive(nums, curr_sum + nums[index], count, mask))
                    mask ^= 1 << index

                # if res:
                #     break
            self.memo[key] = res
            # if key == (0, 0):
            #     print(key)
            #     print(self.memo)


        return self.memo[key]
        
        
            
        
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