<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 {
    bool canPartition (int index, vector<int>& nums, int target, vector<int> & sums) {
        if (index < 0)
            return true;
        for (int i = 0; i < sums.size(); i++) {
            if (sums[i] + nums[index] > target) 
                continue;
            sums[i] += nums[index];
            if (canPartition(index-1, nums, target, sums))
                return true;
            sums[i] -= nums[index];
            if (sums[i]==0) break;
        }
        return false;
    }
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int total = 0;
        for(int n:nums)
            total+=n;
        if (total % k)
            return false;
        int target = total / k;
        vector<int> sums (k);
        std::sort(nums.begin(), nums.end());
        return canPartition(nums.size()-1, nums,target,sums);
    }
};
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