# New-year tree

Medium

Execution time limit is 1 second

Runtime memory usage limit is 64 megabytes

For decoration of the New-year tree Peter has in the order a garland from the n lamps and k of different paints for their painting. How many methods can he to do it, if he must no two identical colors be alongside?

## Input

The amount of lamps is n, the amount of different paints is k (1 ≤ k, n ≤ 15).

## Output

Print the number of painting ways. If Peter can not paint a garland after the described requirements, to show out -1.

## Examples

Input #1

Answer #1

Submissions 11K

Acceptance rate 12%