[Solution] Find eX Solution Codechef

[Solution] Find eX Solution Codechef

Chef has $4$ positive integers $A$, $B$, $C$, and $D$ such that $A$ $\%$ $B=C$ $\%$ $D$.

Find the smallest positive integer $X$ such that $(A+X)$ $\%$ $B=(C+X)$ $\%$ $D$ holds.

It is guaranteed that such $X$ always exists.

Input Format Find eX Solution Codechef

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• The first and only line of each test case contains four space-separated integers $A$, $B$, $C$, and $D$.

Output FormatFind eX Solution Codechef

For each test case, print a single line containing one integer — $X$, the smallest integer satisfying the conditions.

Constraints Find eX Solution Codechef

Sample 1: Find eX Solution Codechef

3
4 7 4 8
5 1 8 2
3 2 4 3

1
2
5

Explanation: Find eX Solution Codechef

Test case $1$: The smallest $X$ satisfying the equation is $1$, as $(4+1)$ $\%$ $7=(4+1)$ $\%$ $8=5$.

Test case $2$: The smallest $X$ satisfying the equation is $2$, as $(5+2)$ $\%$ $1=(8+2)$ $\%$ $2=0$.