D. X-Magic Pair
math; number theory
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.