Problem Statement

You are given \(N\) numbers. Divide them into \(K(\geq 3)\) groups.
Each group must contain at least one number.

ex) For example, if the given numbers are \(\{10,3,23,91,5\}\) and \(K=3\), then
a division such as \(\{\{3,91\},\{23,5\},\{10\}\}\) is valid, while
a division such as \(\{\{\},\{3,5,10\},\{23,91\}\}\) is not allowed.

Compute the average of each group, then from these compute (largest average) - (smallest average),
and finally round the fractional part up; the resulting value is called the "difference of averages".
Find the difference of averages when the grouping is chosen so that the difference of averages is maximized.

Input

\(N\)
\(K\)
\(n_1\)
\(n_2\)
\(\dots\)
\(n_N\)

The \(1\)st line contains \(N\ (3 \leq N \leq 9)\).
The \(2\)nd line contains \(K\ (3 \leq K \leq N)\).
Lines \(3\) through \(N+2\) contain the numbers \((1 \leq n_i \leq 1000, 1 \leq i \leq N)\).

Output

Output the numerical answer as a string.
Print a newline at the end.

Sample

5
3
555
20
432
301
21

535

8
4
329
980
656
738
739
542
873
501

651