<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:
        def backtrack(count, curr_sum, index):
            if count == k - 1:
                return True

            taken_str = "".join(used)

            if curr_sum == target:
                memo[taken_str] = backtrack(count+1, 0, 0)
                return memo[taken_str]

            if curr_sum > target:
                return False

            if taken_str in memo:
                return memo[taken_str]
          
            for i in range(index, n):
                if used[i] == "0":
                    used[i] = "1"
                    if backtrack(count, curr_sum + nums[i], i+1):
                        return True
                    used[i] = "0"
            memo[taken_str] = False

            return False
                    
                        
        total = sum(nums)
        target = total // k
        if target * k != total:
            return False

        n = len(nums)
        used = ["0"] * n
        memo = {}
        return backtrack(0, 0, 0)

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