# Sorting Game

Very easy

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

In The Sorting Game, you are given a sequence containing a permutation of the integers between 1 and n, inclusive. In one move, you can take any k consecutive elements of the sequence and reverse their order. Find the fewest number of moves to sort the sequence in ascending order.

## Input

Consists of multiple test cases. The first line of each test case contains two integers n (2 ≤ n ≤ 8) and k (2 ≤ k ≤ n). The second line of each test case contains a permutation of numbers from 1 to n.

## Output

For each test case print in a separate line the fewest number of moves to sort the sequence in ascending order or -1 if it's impossible.

## Examples

Input #1

Answer #1

Submissions 561

Acceptance rate 45%