<p>You are given an integer array <code>nums</code>​​​ and an integer <code>k</code>. You are asked to distribute this array into <code>k</code> subsets of <strong>equal size</strong> such that there are no two equal elements in the same subset.</p>

<p>A subset&#39;s <strong>incompatibility</strong> is the difference between the maximum and minimum elements in that array.</p>

<p>Return <em>the <strong>minimum possible sum of incompatibilities</strong> of the </em><code>k</code> <em>subsets after distributing the array optimally, or return </em><code>-1</code><em> if it is not possible.</em></p>

<p>A subset is a group integers that appear in the array with no particular order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,1,4], k = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> The optimal distribution of subsets is [1,2] and [1,4].
The incompatibility is (2-1) + (4-1) = 4.
Note that [1,1] and [2,4] would result in a smaller sum, but the first subset contains 2 equal elements.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [6,3,8,1,3,1,2,2], k = 4
<strong>Output:</strong> 6
<strong>Explanation:</strong> The optimal distribution of subsets is [1,2], [2,3], [6,8], and [1,3].
The incompatibility is (2-1) + (3-2) + (8-6) + (3-1) = 6.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,3,3,6,3,3], k = 3
<strong>Output:</strong> -1
<strong>Explanation:</strong> It is impossible to distribute nums into 3 subsets where no two elements are equal in the same subset.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 16</code></li>
	<li><code>nums.length</code> is divisible by <code>k</code></li>
	<li><code>1 &lt;= nums[i] &lt;= nums.length</code></li>
</ul>

class Solution {
public:
    int dp[80000];
    int func(int mask,vector<int> &v,int k){
       int n=v.size();
      
        if(mask==(1<<n)-1) return 0;
        
        if(dp[mask]!=-1) return dp[mask];
         unordered_set<int> s;
         int i,j;
         vector<int> vi;
        for(i=0;i<v.size();i++){
            if((!(mask&(1<<i)))&& s.find(v[i])==s.end()){
                s.insert(v[i]);
                vi.push_back(i);
                 cout<<i<<" ";
            }
           
        }
        //  cout<<mask<<endl;
        if(vi.size()==0) return dp[mask]=0;
         cout<<mask<<endl;
        if(vi.size()<n/k) return dp[mask]=1e9;
        int ans=1e9;
        if(vi.size()==n/k){
             int mk=mask,mx=0,mn=n+1;
              for(i=0;i<vi.size();i++){
                   mk=mk|(1<<vi[i]);
                   mx=max(mx,v[vi[i]]);
                   mn=min(mn,v[vi[i]]);
              }
              ans=min(ans,mx-mn+func(mk,v,k));
            
        }
        else{
            int m=vi.size();
            int l=(1<<m)-1;
            for(i=1;i<=l;i++){
                if(__builtin_popcount(i)==n/k){
                    int mk=mask,mx=0,mn=n+1;
                    for(j=0;j<=m;j++){
                        if((1<<j)&i){
                            mk=mk|(1<<vi[j]);
                             mx=max(mx,v[vi[j]]);
                             mn=min(mn,v[vi[j]]);
                        }
                    }
                     ans=min(ans,mx-mn+func(mk,v,k));
                }
            }
        }
        return dp[mask]=ans;
    }
    int minimumIncompatibility(vector<int>& v, int k) {
        memset(dp,-1,sizeof(dp));
        int ans=func(0,v,k);
        return ans==1e9? -1: ans;
    }
};
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