YSACODE discuss3

You've got array A, consisting of n integers and a positive integer k. Array A is indexed by integers from 1 to n.

You need to permute the array elements so that value

$\text{[math]}$ became minimal possible. In particular, it is allowed not to change order of elements at all.

Input

The first line contains two integers n,k (2≤n≤3·10⁵, 1≤k≤min(5000,n-1)).

The second line contains n integers A[1],A[2],...,A[n] (-10⁹≤A[i]≤10⁹), separate by spaces − elements of the array A.

Output

Print the minimum possible value of the sum described in the statement.

Examples

Input

3 2
1 2 4

Output

Input

5 2
3 -5 3 -5 3

Output

Input

6 3
4 3 4 3 2 5

Output

Note

In the first test one of the optimal permutations is 142.

In the second test the initial order is optimal.

In the third test one of the optimal permutations is 234435.