Problem Description

Alexander The great, while roaming the stretch of Turkey, came across a wise man.

He asked the wise man, “Who is the greatest conqueror of all?”. The wise man replied, “A person with great

strength and intelligence. Whosoever can solve my puzzle will go on to become the greatest!”. The puzzle is as

follows; Given two integers ‘n1’ and ‘n2’, select two integers ‘a’ and ‘b’, such as to solve the equation (n1 * a +

n2 * b = x). But there is a catch, ‘x’ is the smallest positive integer which satisfies the equation. Can you help

Alexander become the greatest?

Constraints

1 <= T <= 1000

-10^7 <= a, b <= 10^7

0 <= n1, n2 <= 10^7

Input Format

The first line contains the number of Test cases T.

Next T lines contains two space-separated integers, n1 and n2.

Output

Print the value of x.

Test Case

Explanation

Example 1

Input

1

34818 45632

Output

2

Explanation

Given n1 = 34818 and n2 = 45632, if we choose a = 3553 and b = -2711, we get

=> n1 * a + n2 * b = x

=> 34818 * 3553 + 45632 * (-2711)

=> 2

Note: No other value of a and b, within the range, will give smaller value than 2

I know if two number are odd and there modulos is not zero so the result will be 1 and if two number give modulus zero there answer will be the same smalller number and if both are even and do not give modulos zero there answer will be 2… But i just want know how to deal with this range… If gcd of number goes out of range, how can i calculate the answer…