<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>

const int MAX_LENGTH = 16;
int SIZE;
int SIDE_SIZE;
int K;

class Solution {
public:
    bool dfs(const std::vector<int>& xs, std::bitset<MAX_LENGTH> mask, int side, int c, std::unordered_map<int, bool>& memo)
    {  

        if(c == K)
          return true;

        if(side > SIDE_SIZE)
          return false;
        
        if(auto i = memo.find((int)mask.to_ulong()); i != memo.end())
          return (*i).second; 

        bool ans = false;
        for(int i = 0; i < SIZE && !mask.all() && !ans; i++)
        {
            if(mask.test(i)) continue;
            mask.set(i);
            if(side + xs[i] == SIDE_SIZE)
                ans |= memo[(int)mask.to_ulong()] = dfs(xs, mask, 0, c + 1, memo);
            ans |= memo[(int)mask.to_ulong()] = dfs(xs, mask, side + xs[i], c, memo);
            mask.set(i, false);
        }
        return ans;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        SIZE = nums.size();
        K = k;
        int perimeter = std::reduce(nums.begin(), nums.end());
        if(SIZE < k || (perimeter % k))
          return false;
        SIDE_SIZE = perimeter / K;
        std::sort(nums.begin(), nums.end(), std::greater<int>());
        std::bitset<MAX_LENGTH> mask;
        std::unordered_map<int, bool> memo;
        return dfs(nums, mask, 0, 0, memo);
    }
};
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