<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:
    vector<int> a;
    int t1;
    vector<int> dp;
    int choose_k(int i,int mask,int mn,int mx,int t,int k){
        if(t==0 && k==1){
            return mx-mn;
        }
        if(t==0){
            if(dp[mask]<-1) dp[mask]=choose_k(0,mask,INT_MAX,INT_MIN,t1,k-1);
            int x=dp[mask];
            return x==-1?-1: mx-mn+x;
        }
        if(i>=a.size()) return -1;
        if(mask&(1<<i)) return choose_k(i+1,mask, mn,mx,t,k);//already chosen
        int nxti=i;
        while(nxti<a.size() && a[nxti]==a[i]) nxti++;//for unique number
        int m1=-1,m2=-1;
        m1=choose_k(nxti,mask|(1<<i),min(mn,a[i]),max(mx,a[i]),t-1,k);
        m2=choose_k(nxti,mask,mn,mx,t,k);//not chosing
        if(m1==-1 && m2==-1) return -1;
        if(m1==-1) return m2;
        if(m2==-1) return m1;
        return min(m1,m2);
    }
    int minimumIncompatibility(vector<int>& nums, int k) {
        sort(nums.begin(),nums.end());
        a=nums;
        if(a.size()%k!=0) return -1;
        t1=a.size()/k;
        dp.resize((1<<a.size()),-2);
        return choose_k(0,0,INT_MAX,INT_MIN,t1,k);
    }
};
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