Finite or not?

### 题目描述 有 $n$ 组数据，每一组数据读入一个分数的分子 $p$、分母 $q$ 和进制 $b$（分子、分母均以十进制读入）求在 $b$ 进制下 $\frac{p}{q}$ 是否为有限小数。如果是，输出 `Finite`，否则输出 `Infinite` ### 输入格式 第一行输入 $n$ 接下来 $n$ 行输入 $p$, $q$ 和 $b$。 ### 输出格式 对于每一组数据，输出 `Finite` 或 `Infinite` 1 <= n <= 10^5, 1 <= b, p, q <= 10^18 由 @Medoric 提供翻译

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.

2
6 12 10
4 3 10

Finite
Infinite

4
1 1 2
9 36 2
4 12 3
3 5 4

Finite
Finite
Finite
Infinite

$ \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 $