<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>

from typing import List


class Solution:
    def minimumIncompatibility(self, nums: List[int], k: int) -> int:
        a = sorted(nums)

        d = [99999999999999999999999 for _ in range(1<<len(a))]

        elements = []
        import collections

        q = collections.deque()

        for i in range(1<<len(a)):
            count = 0
            smallest = 9999999999999999999999
            largest = -999999999999999999999
            same = None
            for j in range(len(a)):
                if (i & (1<<j))>0:
                    if a[j] == same:
                        count = -1
                        break
                    count+=1
                    same= a[j]
                    smallest = min(smallest,a[j])
                    largest = max(largest,a[j])
            if count == len(a)//k:
                elements.append((i,largest-smallest))
                d[i]=largest-smallest
                q.append((i,largest-smallest))



        next = collections.deque()
        d[0]=0
        while len(q)>0:
            state,amount = q[0]
            q.popleft()
            if amount!=d[state]:
                continue

            for i,fff in elements:
                if (i&state)==0:
                    newstate = i +state
                    if d[newstate]>d[state]+fff:
                        d[newstate]=d[state]+fff
                        next.append((newstate,d[newstate]))

            if len(q)==0:
                if len(next)==0:
                    break
                q = next
        if d[-1]==99999999999999999999999:
            return -1
        return d[-1]
18600