<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>

from pprint import pprint


class Solution:
    def canPartitionKSubsets(self, nums: List[int], k: int) -> bool:
        total_sum = sum(nums)

        if total_sum % k != 0:
            return False

        target_sum = total_sum // k
        n = len(nums)
        num_subsets = 1 << n

        dp = [[False] * (k + 1) for _ in range(num_subsets)]
        dp[0][0] = True
        current_sum = [0] * num_subsets

        for mask in range(num_subsets):
            for j in range(k):
                if not dp[mask][j]:
                    continue

                for i in range(n):
                    new_mask = mask | (1 << i)
                    new_sum = current_sum[mask] + nums[i]

                    if mask == new_mask or new_sum > target_sum:
                        continue

                    current_sum[new_mask] = new_sum % target_sum

                    if current_sum[new_mask] == 0:
                        dp[new_mask][j + 1] = True
                    else:
                        dp[new_mask][j] = True

        return dp[num_subsets - 1][k]

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