<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 = 1e9+7;
class Solution {
public:
    int dp[1<<16];
    vector<int> masks;
    map<int,int> incomp;
    int n;
    int solve(int m){
        if(__builtin_popcount(m) == n){
            return 0;
        }
        if(~dp[m]) return dp[m];
        int val = inf;
        for(auto mask:masks){
            if(!(m&mask)){
                val = min(val,incomp[mask]+solve(m|mask));
            }
        }
        return dp[m]=val;
    }
    int minimumIncompatibility(vector<int>& nums, int k) {
        n = nums.size();
        memset(&dp,-1,sizeof dp);
        for(int i=0;i<(1<<n);i++){
            set<int> temp;
            for(int j=0;j<n;j++){
                if((i>>j)&1){
                    temp.insert(nums[j]);
                }
            }
            if(__builtin_popcount(i) == temp.size() and __builtin_popcount(i) == n/k){
                masks.push_back(i);
                incomp[i]= *temp.rbegin() - *temp.begin();
                // cout<<i<<" "<<incomp[i]<<endl;
            }
        }
        return solve(0)<inf?solve(0):-1;
    }
};
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