<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 {
public:
    unordered_map<int, bool> memo;
    bool canPartitionKSubsets(vector<int>& nums, int index, int curr_sum, int target_sum, int count, int k, int& mask){
        if(count == k - 1){
            return true;
        }

        if(curr_sum > target_sum){
            return false;
        }

        if(memo.find(mask) != memo.end()){
            return memo[mask];
        }

        if(curr_sum == target_sum){
            return canPartitionKSubsets(nums, 0, 0, target_sum, count + 1, k, mask);
        }

        for(int i = index; i < nums.size(); i++){
            if(mask & (1 << i)){
                continue;
            }

            mask |= 1 << i;
            if(canPartitionKSubsets(nums, i + 1, curr_sum + nums[i], target_sum, count, k, mask)){
                memo[mask] = true;
                return true;
            }
            mask &= ~(1 << i);
        }
        return memo[mask] = false;
    }

    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        if(sum%k != 0){
            return false;
        }
        sort(nums.begin(), nums.end());
        int mask = 0;
        return canPartitionKSubsets(nums, 0, 0, sum/k, 0, k, mask);
    }
};
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