<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 rec(int i,vector<int> &nums,int k,vector<int> &v,int s)
    {
        int n=nums.size();
        if(i==n)
        {
            for(int j=0;j<k;j++)
                if(v[j]!=v[0]) return false;
            return true;
        }
        bool ans=false;
        unordered_map<int,int> M;
        for(int j=0;j<k;j++)
        {
            if(M[v[j]]) continue;
            M[v[j]]=1;
            if(v[j]+nums[i]>s/k) continue;
            v[j]+=nums[i];
            ans|=rec(i+1,nums,k,v,s);
            v[j]-=nums[i];
            if(ans) return ans;
        }
        return ans;
    }

    bool canPartitionKSubsets(vector<int>& nums, int k) {
        vector<int> v(k,0);
        int s=0;
        if(nums.size()<k) return false;
        for(auto i:nums) s+=i;
        if(s%k!=0) return false;
        sort(nums.begin(),nums.end());
        reverse(nums.begin(),nums.end());
        for(auto i:nums)
            if(i>s/k) return false;
        return rec(0,nums,k,v,s);
    }
};
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