Lcm hates Gcd Codechef Solution

Problem

Chef has two integers $A$ and $B$.
Chef wants to find the minimum value of $\text{lcm}(A,X)-\text{gcd}(B,X)$ where $X$ is any positive integer.

Help him determine this value.

Note: $\text{gcd}(P,Q)$ denotes the greatest common divisor of $P$ and $Q$ and $\text{lcm}(P,Q)$ denotes the least common multiple of $P$ and $Q$.

Input Format

• The first line contains a single integer $T$ — the number of test cases. Then the test cases follow.
• The first and only line of each test case contains two space-separated integers $A$ and $B$ — the integers mentioned in the statement.

Output Format

For each test case, output the minimum value of $\text{lcm}(A,X)-\text{gcd}(B,X)$.

Constraints

Sample 1:

3
12 15
5 50
9 11

9
0
8

Explanation:

Test case $1$: For $X=6$: $\text{lcm}(12,6)-\text{gcd}(15,6)=12-3=9$ which is the minimum value required.

Test case $2$: For $X=50$: $\text{lcm}(5,50)-\text{gcd}(50,50)=50-50=0$ which is the minimum value required.

Test case $3$: For $X=1$: $\text{lcm}(9,1)-\text{gcd}(11,1)=9-1=8$ which is the minimum value required.