X-Magic Pair

题意翻译

给一个数对 $(a,b)$ ，每次可以进行操作 $(a,b) \to (|a-b|,b)$ 或 $(a,|a-b|)$ 。问最后能否令 $a=x$ 或 $b=x$ 。$a,b,x \le 10^{18}$

题目描述

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.

输入输出格式

输入格式

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} $ ).

输出格式

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

输入输出样例

输入样例 #1

8
6 9 3
15 38 7
18 8 8
30 30 30
40 50 90
24 28 20
365 216 52
537037812705867558 338887693834423551 3199921013340

输出样例 #1

YES
YES
YES
YES
NO
YES
YES
YES