<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>

const int inf = 1e8 ;
class Solution {
public:
    
    int minimumIncompatibility(vector<int>& nums, int k) {
        int n = nums.size() ;
        int pos[1<<n] ;
        for(int i =1;i<(1<<n);i++){
            pos[i] = inf ;
            vector<int> ct(n+1) ;
            int mn = 1000,mx = 0 ;
            for(int j =0;j<n;j++){
                if((1<<j)&i){
                    ct[nums[j]]++ ;
                    if(ct[nums[j]]>1){
                        mx = inf,mn = 0 ;
                    }
                    mx = max(mx,nums[j]) ;
                    mn = min(mn,nums[j]) ;
                }
            }
            pos[i] = mx-mn ;
        }
        int dp[(1<<n)] ;
        dp[0] = 0 ;
        int req = n/k ;
        for(int j = 1;j<(1<<n);j++){
            dp[j] = inf ;
            int count = __builtin_popcount(j) ;
            if(count%req!=0)continue ;
            int i = count/req ;
            int mask = j ; 
            while(mask){
                count = __builtin_popcount(mask) ;
                if(count==req){
                    dp[j] = min(dp[j],pos[mask]+dp[j^mask]) ;
                }
                mask = ((mask-1)&j) ;
            }
        }
        
        return (dp[(1<<n)-1]==inf?-1:dp[(1<<n)-1]) ;

    }
};
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