Problem Statement

On Nsukumi Island, peace is maintained by a peculiar ecosystem.

・$n$ animals live there.
・Animal $i$ can prey on animal $i+1$ ($1 \le i \le n-1$).
・Animal $n$ can prey on animal $1$.

Since the animals do not want to be preyed upon, they have made an arrangement that acts as a mutual deterrent.
That is, they have agreed to always maintain a situation in which every animal, if it is a predator, is also prey.

Now, the animals of Nsukumi Island are considering moving to New Nsukumi Island.
The move is carried out using $n$ boats, each carrying at most $m$ animals, according to the following procedure.
・All boats are initially at Nsukumi Island.
・A boat can travel between Nsukumi Island and New Nsukumi Island in exactly $1$ day one way, provided that at least $1$ animal is on board.
・Because of the risk of collision, $2$ or more boats cannot be out at sea at the same time on $1$ day.
・The move ends when all the animals have arrived at New Nsukumi Island.
・It is not necessary to use all the boats. That is, leftover boats may be abandoned on Nsukumi Island.

Find the minimum number of days required to complete the move while keeping the arrangement.
If the move is impossible, output $-1$.

Input

n m

$2 \le n \le 100000$
$2 \le m \le 50$

Output

Find the minimum number of days required to complete the move while keeping the arrangement.
If the move is impossible, output $-1$.
Print a newline at the end.

Sample

3 2

-1

3 3

1