<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:
        subset_sum = sum(nums)//k
        if sum(nums) % k != 0:
            return False
        # print("herr")
        taken = [0]*len(nums)
        counts = collections.defaultdict(int)
        for i, n in enumerate(nums):
            # counts[n] += 1
            taken[i] += 1

        cache = dict()
        def backtrack(subsets_num, curr_sum, curr_dict):
            if (subsets_num, curr_sum, ''.join(map(str, curr_dict))) in cache:
                return cache[(subsets_num, curr_sum, ''.join(map(str, curr_dict)))]

            # print("b", subsets_num, curr_sum, curr_dict)
            # print("curr_dict.values()", curr_dict.values())
            if sum(curr_dict) == len(nums) and subsets_num == k:
                # print("inss")
                return True

            for idx in range(len(nums)):
                # if curr_dict[nums[idx]] < counts[nums[idx]]:
                if curr_dict[idx] < taken[idx]:
                    if curr_sum + nums[idx] <= subset_sum:
                        curr_sum += nums[idx]
                        # curr_dict[nums[idx]] += 1
                        curr_dict[idx] += 1
                        if curr_sum == subset_sum:
                            if backtrack(subsets_num + 1, 0, curr_dict):
                                return True
                        elif curr_sum < subset_sum:
                            if backtrack(subsets_num , curr_sum, curr_dict):
                                return True 
                        curr_sum -= nums[idx]
                        # curr_dict[nums[idx]] += 1
                        curr_dict[idx] -= 1

            cache[(subsets_num, curr_sum, ''.join(map(str, curr_dict)))] = False
            return False

        # return backtrack(0, 0, collections.defaultdict(int))
        return backtrack(0, 0, [0]*len(nums))        
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