An Important Scientific Number

Interview

Time limit2sMemory limit1024 MB

Summary

Given gear sizes a and b, find the smallest non-negative x so that b divides a+x and a divides b+x.

Level: Medium4 of 10
Topics: Number theory, Math
Solved: No attempts yet

Statement

Ping was assembling his very important new invention when he realized he had made a mistake in one of the formulas, and the corresponding gear may have been assembled incorrectly.

After looking closely at the part and fixing the formula, Ping noticed that the part currently has two gears with $a$ and $b$ teeth. To work correctly, the gears must have $a + x$ and $b + x$ teeth, where $x$ is a non-negative integer such that $a + x$ is divisible by $b$ and $b + x$ is divisible by $a$ .

Ping is very tired, so he asks you to find a non-negative $x$ that satisfies these conditions. Ping does not like large gears, so among all suitable values of $x$ , choose the smallest one.

Input

A single line contains two space-separated integers $a$ and $b$ , the sizes of the gears in the part ( $1 \le a, b \le 10^9$ ).

Output

Print one integer $x$ , the smallest non-negative value that satisfies the conditions. This is the minimum number of teeth the gears are missing for the invention to work correctly.

Examples4

Example 1
Input
```
10 5
```
Expected output
```
5
```
Example 2
Input
```
8 1
```
Expected output
```
7
```
Example 3
Input
```
3 4
```
Expected output
```
5
```
Example 4
Input
```
123 123
```
Expected output
```
0
```