<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 {
    std::vector<std::unordered_map<std::bitset<16>, bool>> m_dp;
    
    bool dfs(const std::vector<int>& values, int sum, int target, int k, std::bitset<16>& bs) {
        if (k == 0)
            return true;
        
        if (m_dp[k].end() != m_dp[k].find(bs))
            return m_dp[k][bs];
        
        bool result = false;
        
        for (int i = 0; i < static_cast<int>(values.size()); ++i) {
            if (!bs[i]) {
                bs[i] = true;
                sum += values[i];
                
                if (sum == target)
                    result = dfs(values, 0, target, k - 1, bs);
                else if (sum < target)
                    result = dfs(values, sum, target, k, bs);
                
                sum -= values[i];
                bs[i] = false;
            }
            
            if (result)
                break;
        }
        
        m_dp[k][bs] = result;
        
        return result;
    }
    
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        std::sort(nums.begin(), nums.end());
        
        const auto total = std::accumulate(nums.begin(), nums.end(), 0);
        
        if (total % k != 0)
            return false;
        
        m_dp = std::vector<std::unordered_map<std::bitset<16>, bool>>(k + 1);
        
        std::bitset<16> bs;
        return dfs(nums, 0, total / k, k, bs);
    }
};
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