<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 canPartitionKSubsets(vector<int>& nums, int k) {
        int sum = 0, n = nums.size();
        for(int i=0; i<n; i++) sum += nums[i];
        if(sum % k) return false;
        sum /= k;
        sort(begin(nums),end(nums));
        if(nums.back() > sum) return false;

        vector<int> dp(1<<n), tot(1<<n);
        dp[0] = 1;
        for(int i=0; i<(1<<n); i++) {
            if(dp[i]) {
                for(int j=0; j<n; j++) {
                    if(i>>j&1)continue;
                    if(nums[j]<=(sum-(tot[i]%sum))) {
                        dp[i|1<<j] = true;
                        tot[i|1<<j] = nums[j]+tot[i];
                    } else break;
                }
            }
        }
        return dp[(1<<n)-1];
        

    }
};
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