Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

F. Goats and Wolves

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOnce Vasya needed to transport *m* goats and *m* wolves from riverbank to the other as quickly as possible. The boat can hold *n* animals and Vasya, in addition, he is permitted to put less than *n* animals in the boat. If in one place (on one of the banks or in the boat) the wolves happen to strictly outnumber the goats, then the wolves eat the goats and Vasya gets upset. When Vasya swims on the boat from one shore to the other, he must take at least one animal to accompany him, otherwise he will get bored and he will, yet again, feel upset. When the boat reaches the bank, first all the animals get off simultaneously, and then the animals chosen by Vasya simultaneously get on the boat. That means that at the moment when the animals that have just arrived have already got off and the animals that are going to leave haven't yet got on, somebody might eat someone. Vasya needs to transport all the animals from one river bank to the other so that nobody eats anyone and Vasya doesn't get upset. What is the minimal number of times he will have to cross the river?

Input

The first line contains two space-separated numbers *m* and *n* (1 ≤ *m*, *n* ≤ 10^{5}) — the number of animals and the boat's capacity.

Output

If it is impossible to transport all the animals so that no one got upset, and all the goats survived, print -1. Otherwise print the single number — how many times Vasya will have to cross the river.

Examples

Input

3 2

Output

11

Input

33 3

Output

-1

Note

The first sample match to well-known problem for children.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/23/2017 04:14:50 (c4).

Desktop version, switch to mobile version.
User lists

Name |
---|