Diagonal Across Tiles

Time limit1sMemory limit128 MB

Summary

Given a grid of x by y unit tiles, count how many tiles a diagonal from corner to corner passes through using the gcd formula.

Level: Easy3 of 10
Topics: Math, Number theory
Solved: No attempts yet

Problem

Unit square tiles with side length 1cm are used to fill an xcm by ycm rectangular wall without gaps. x and y are positive integers.

A diagonal is drawn from one corner of the rectangle to the opposite corner. Among all x * y tiles, determine how many tiles the diagonal passes through.

Input

The first line contains the rectangle width x and height y. x and y are positive integers no greater than 1,000,000,000, and there is at least one space between them.

Output

Print the number of tiles that the diagonal passes through.

Examples2

Example 1
Input
```
8 12
```
Expected output
```
16
```
Example 2
Input
```
5 6
```
Expected output
```
10
```