<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>

#define ll long long
#define pb push_back
class Solution {
public:
    ll f(ll bitmask,vector<ll>& possible,unordered_map<ll,ll>& mp,ll mask,vector<ll>& dp){
        if(dp[bitmask]!=-1){
            return dp[bitmask];
        }
        if(bitmask==mask){
            return dp[bitmask]=0;
        }
        ll mini=1e5;
        for(ll i=0;i<possible.size();i++){
            if((possible[i] & bitmask)==0){
                ll ca = mp[possible[i]]+f((bitmask|possible[i]),possible,mp,mask,dp);
                mini=min(mini,ca);
            }
        }
        return dp[bitmask]=mini;
    }
    int minimumIncompatibility(vector<int>& nums, int k) {
        ll n = nums.size();
        ll mask = ((1<<n)-1);

        vector<ll>possible;
        unordered_map<ll,ll>mp;
        for(ll i=0;i<=mask;i++){
            if(__builtin_popcount(i)==n/k){
                set<ll>st;
                for(ll j=0;j<n;j++){
                    if(((1<<j)&i)!=0){
                        st.insert(nums[j]);
                    }
                }
                if(st.size()==n/k){
                    possible.pb(i);
                    ll a = (*st.begin());
                    auto b1 = st.end();
                    b1--;
                    ll b = (*b1);
                    mp[i]=b-a;
                }
            }
        }

        vector<ll>dp(mask+1,-1);
        for(auto it:mp){
            cout<<it.first<<" "<<it.second<<endl;
        }
        ll ans = f(0,possible,mp,mask,dp);
        if(ans>=1e5)ans=-1;
        return ans;
        
    }
};
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