A14712 | X-Magic Pair

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) $b := |a - b|$ ,

where $|a - b|$ is the absolute difference between $a$ and $b$ .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.

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 $x$ ( $1 \le a, b, x \le 10^{18}$ ).

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