Neko does Maths

Description:

Input:

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

Output:

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.

Sample Input:

6 10

Sample Output:

2

Sample Input:

21 31

Sample Output:

9

Sample Input:

5 10

Sample Output:

0

Note:

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.