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?
The amount of lamps is n, the amount of different paints is k (1 ≤ k, n ≤ 15).
Print the number of painting ways. If Peter can not paint a garland after the described requirements, to show out -1.
Input example #1
Output example #1