You are given a pair of integers $(a, b)$ and an integer $x$.

You can change the pair in two different ways:

• set (assign) $a := |a - b|$;
• set (assign) $b := |a - b|$,

The pair $(a, b)$ is called $x$-magic if $x$ is obtainable either as $a$ or as $b$ using only the given operations (i.e. the pair $(a, b)$ is $x$-magic if $a = x$ or $b = x$ after some number of operations applied). You can apply the operations any number of times (even zero).

Your task is to find out if the pair $(a, b)$ is $x$-magic or not.

You have to answer $t$ independent test cases.

Input

The first line of the input contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The next $t$ lines describe test cases.

The only line of the test case contains three integers $a$, $b$ and $x$ ($1 \le a, b, x \le 10^{18}$).

Output

For the $i$-th test case, print YES if the corresponding pair $(a, b)$ is $x$-magic and NO otherwise.

见题面 Input 部分

见题面 Output 部分