CF983A Finite or not?

You are given several queries. Each query consists of three integers $ p $ , $ q $ and $ b $ . You need to answer whether the result of $ p/q $ in notation with base $ b $ is a finite fraction. A fraction in notation with base $ b $ is finite if it contains finite number of numerals after the decimal point. It is also possible that a fraction has zero numerals after the decimal point.

The first line contains a single integer $ n $ ( $ 1 \le n \le 10^5 $ ) — the number of queries. Next $ n $ lines contain queries, one per line. Each line contains three integers $ p $ , $ q $ , and $ b $ ( $ 0 \le p \le 10^{18} $ , $ 1 \le q \le 10^{18} $ , $ 2 \le b \le 10^{18} $ ). All numbers are given in notation with base $ 10 $ .

For each question, in a separate line, print Finite if the fraction is finite and Infinite otherwise.

$ \frac{6}{12} = \frac{1}{2} = 0,5_{10} $ $ \frac{4}{3} = 1,(3)_{10} $ $ \frac{9}{36} = \frac{1}{4} = 0,01_2 $ $ \frac{4}{12} = \frac{1}{3} = 0,1_3 $