On some island each inhabitant is either a knight who only tells the truth, or a liar who always lies. Also, on the island there exists a university of technology where some of the inhabitants work. All of the university employees will always tell you the following two things, no matter which employee you ask:

It is also known that no two employees of the university have an identical salary, and no two work equally. Write a program which will compute how many persons are employed by this university.

Input

The only input line contains two integers N and M, with one space between them [N, M <= 1000000000].

Output

The output must contain only one integer - the total number of employees of this university, or 0 if there is no way to find the number of employees.

Example

Input:
1 1

Output:
2

Author: Filimonenkov D.O.