Codeforces Round #483 (Div. 2)C题

C. Finite or not?

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given several queries. Each query consists of three integers $p$

, $\mathrm{q\; and\; b.\; You\; need\; to\; answer\; whether\; the\; result\; of\; p/q\; in\; notation\; with\; base\; b}$

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.

Input

The first line contains a single integer $n$

$\mathrm{(1\le n\le 105}$) — the number of queries.

Next $n$$\mathrm{lines\; contain\; queries,\; one\; per\; line.\; Each\; line\; contains\; three\; integers\; p,\; q,\; and\; b\; (0\le p\le 1018,\; 1\le q\le 1018,\; 2\le b\le 1018).}$

$\mathrm{All\; numbers\; are\; given\; in\; notation\; with\; base\; 10}$

.

Output

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

Examples

Input

Copy

2
6 12 10
4 3 10

Output

Copy

Finite
Infinite

Input

Copy

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

Output

Copy

Finite
Finite
Finite
Infinite

Note

$\frac{\mathrm{612=12=0,510}}{}$

$\frac{\mathrm{43=1,(3)10}}{}$

$\frac{\mathrm{936=14=0,012}}{}$

$\frac{\mathrm{412=13=0,13}}{}$

$\frac{\mathrm{\#include\; <iostream>\#include\; <cstdio>\#include\; <cstring>\#include\; <cstdlib>\#include\; <algorithm>\#include\; <vector>\#include\; <math.h>//codeforcesusing\; namespace\; std;int\; main()\{ \; ios::sync\_with\_stdio(false); \; int\; n; \; long\; long\; p,q,b,temp; \; cin>>n; \; while(n--)\{ \; cin>>p>>q>>b; \; temp=\_\_gcd(p,q); \; p/=temp;q/=temp; \; int\; flag=1; \; while(1)\{ \; if(q==1)\{ \; break; \; \} \; temp=\_\_gcd(q,b); \; if(temp==1)\{ \; cout<<"Infinite"<<endl; \; flag=0;break; \; \} \; while(q\%temp==0)\{ \; q/=temp; \; \} \; \} \; if(flag)\; cout<<"Finite"<<endl; \; \} \; return\; 0;\}}}{}$