For decoration of the New-year tree Peter has in the order a garland from the N lamps and К of different paints for their painting. How many methods can he to do it, if he must no 2 identical colors be alongside?

Input

The amount of lamps is N, the amount of different paints is К. (1 ≤ K, N ≤ 15).

Output

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