Neko does Maths

题意翻译

给定两个正整数$a,b$，找到非负整数$k$使$a+k$与$b+k$的最小公倍数最小，如有多解输出最小的$k$

题目描述

Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher. Neko has two integers $ a $ and $ b $ . His goal is to find a non-negative integer $ k $ such that the least common multiple of $ a+k $ and $ b+k $ is the smallest possible. If there are multiple optimal integers $ k $ , he needs to choose the smallest one. Given his mathematical talent, Neko had no trouble getting Wrong Answer on this problem. Can you help him solve it?

输入输出格式

输入格式

The only line contains two integers $ a $ and $ b $ ( $ 1 \le a, b \le 10^9 $ ).

输出格式

Print the smallest non-negative integer $ k $ ( $ k \ge 0 $ ) such that the lowest common multiple of $ a+k $ and $ b+k $ is the smallest possible. If there are many possible integers $ k $ giving the same value of the least common multiple, print the smallest one.

输入输出样例

输入样例 #1

6 10

输出样例 #1

2

输入样例 #2

21 31

输出样例 #2

9

输入样例 #3

5 10

输出样例 #3

0

说明

In the first test, one should choose $ k = 2 $ , as the least common multiple of $ 6 + 2 $ and $ 10 + 2 $ is $ 24 $ , which is the smallest least common multiple possible.