<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 len(nums) == 0:
            return False
        
        nums.sort(reverse=True)

        total_sum = sum(nums)

        if total_sum % k != 0:
            return False
        
        target_sum = total_sum // k

        seen = dict()
        n = len(nums)
        ind_map = 0

        def backtrack(index, current_sum, target_sum, subset_num):
            nonlocal ind_map
            if index == n:
                return False

            if current_sum>target_sum:
                seen[ind_map] = False
                return False

            if current_sum == target_sum:
                seen[ind_map] = backtrack(0, 0, target_sum, subset_num + 1)
                return seen[ind_map]
            
            if subset_num == k-1:
                seen[ind_map] = True
                return True
            
            if ind_map in seen:
                return seen[ind_map]

            for i in range(index, n):
                if ((ind_map >> i) & 1) == 0:
                    ind_map |= (1<<i)
                    res = backtrack(i+1, current_sum+nums[i], target_sum, subset_num)
                    if res is True:
                        seen[ind_map] = True
                        return True
                    else:
                        ind_map ^= (1<<i)
            
            return False
        
        return backtrack(0, 0, target_sum, 0)
                    
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