Algorithms and Data Structures

The number of grid points on a segment

Given a segment connecting and , you are asked to calculate the number of grid points (points with integer coordinates) the line crosses.
When calculating the number of grid points, you should exclude the coordinate from the answer.
 
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Input

The only line of the input contains two integers x and y (1 ≤ x, y ≤ ).

Output

The program should print the number of grid points the line crosses.

Examples

Input
Output
8 12
4
12 8
4
 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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