New-year tree

Time limit 1 second

Memory limit 64 MiB

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 data

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

Output data

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

Examples

Input example #1

6 2

Output example #1