Minimizing the LCM

Time limit1sMemory limit256 MB

Summary

Find the smallest N of at least 1 that minimizes the least common multiple of A+N and B+N.

Level: Medium6 of 10
Topics: Number theory, Math
Solved: No attempts yet

Problem

You are given two natural numbers $A$ and $B$ . Find the natural number $N$ that makes the least common multiple of $A + N$ and $B + N$ as small as possible.

Input

The first line contains two natural numbers $A$ and $B$ , separated by a space. $1 \le A, B \le 10^9$ .

Output

Print $N$ on the first line. If several values of $N$ make the least common multiple minimal, print the smallest one.

Note

A natural number is an integer of at least 1, so $N \ge 1$ .

Examples2

Example 1
Input
```
4 10
```
Expected output
```
2
```
Example 2
Input
```
6 15
```
Expected output
```
3
```