Problems

# New-year tree

# New-year tree

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

2