There are three integers $A, B$ and $C$ written on the blackboard.

You can perform the following two operations as many times as you like:

1. Change $B$ to $A-B$.

2. Change $C$ to $B-C$.

Please note that each time you don't need to perform all two operations. You can choose one type of operation to perform.

You are given an integer $x$. Answer whether you can change $C$ into $x$ using these operations.

You need to answer $T$ queries independently.

The first line contains a positive integer $T(1\leq T\leq 10 ^ 5)$.

Each of the next $T$ lines contains four integers $A, B, C, x(-10 ^ 8 \leq A, B, C, x \leq 10 ^ 8)$.

For each test case, output "Yes" if $C$ can become $x$, and "No" otherwise (without quotes).

Please note that $A, B, C, x$ could be negative.