<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:
    bool used[16];

    bool solve(vector<int> nums, int k, int index, int sum, int total){
        if(k == 0) return  true;
        if(total == sum)
            return solve(nums, k - 1, 0, sum, 0);
        for(int i = index; i < nums.size(); i++){
            if(used[i] || total + nums[i] > sum) continue;
            used[i] = true;
            if(solve(nums, k, i + 1, sum, total + nums[i])) return true;
            used[i] = false;
            if(total == 0) return false;
        }
        return false;		
    }

    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = 0;
        for(int i = 0; i < nums.size(); i++) sum += nums[i];
        if(sum % k != 0) return false;
        return solve(nums, k, 0, sum / k, 0);      
    }
};
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