<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 {
    int target;
    unordered_map<string, bool> memo;
    
    bool solve(int currSum, int k, vector<int>& nums, int usedMask) {
        if (k == 0) return true;
        if (currSum == target) return solve(0, k - 1, nums, usedMask);
        
        string key = to_string(currSum) + "," + to_string(k) + "," + to_string(usedMask);
        if (memo.count(key)) return memo[key];
        
        for (int i = 0; i < nums.size(); i++) {
            if (usedMask & (1 << i)) continue;
            if (currSum + nums[i] > target) continue;
            
            if (solve(currSum + nums[i], k, nums, usedMask | (1 << i))) {
                return memo[key] = true;
            }
        }
        
        return memo[key] = false;
    }
    
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        if (sum % k != 0) return false;
        
        target = sum / k;
        int usedMask = 0;
        
        return solve(0, k, nums, usedMask);
    }
};

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