<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[1001000];
    int solve(int mask,vector<vector<int>>&v,int n){
      
        if(mask==((1<<n)-1)) return 0;
        //if(i==v.size()) return 1e9;
        if(dp[mask]!=-1) return dp[mask];
        int ans=1e9;
        for(int i=0;i<v.size();i++){
            if((mask&v[i][0])==0){
                 ans=min(ans,v[i][1]+solve(mask|v[i][0],v,n));
            }
        }
        return dp[mask]=ans;
    }
    int minimumIncompatibility(vector<int>& nums, int k) {
       memset(dp,-1,sizeof(dp));
        int n=nums.size();
        vector<vector<int>>v;
        int r=n/k;
        for(int i=0;i<(1<<n);i++){
            if(__builtin_popcount(i)==(n/k)){
                int maxnum=-1e9,minnum=1e9;
                set<int>st;
                for(int j=0;j<nums.size();j++){
                    if((i&(1<<j))!=0){
                        st.insert(nums[j]);
                        maxnum=max(maxnum,nums[j]);
                        minnum=min(minnum,nums[j]);
                    }
                }
                if(st.size()==(n/k)) {
                    v.push_back({i,maxnum-minnum});
                }

            }
        }
        cout<<v.size()<<endl;
        return solve(0,v,n)==1e9?-1:solve(0,v,n);
    }
};
25000