CF984C Finite or not?

原题链接：http://codeforces.com/contest/984/problem/C

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.

Input

The first line contains a single integer $n (1≤n≤10^5)$ — the number of queries.

Next $n$ lines contain queries, one per line. Each line contains three integers $p, q$, and $b (0≤p≤10^{18},1≤q≤10^{18}, 2≤b≤10^{18})$. 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

2
6 12 10
4 3 10

output

Finite
Infinite

input

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

output

Finite
Finite
Finite
Infinite

Note

$\frac{6}{12}=\frac{1}{2}=0,5_{10}$

$\frac{4}{3}=1,(3)_{10}$

$\frac{9}{36}=\frac{1}{4}=0,01_2$

$\frac{4}{12}=\frac{1}{3}=0,1_3$

题解

先约一波分，如果$q$的质因数都是$b$的因数，那么$\frac{p}{q}$在$b$进制下就是有限的。

但是值域是$10^{18}$，直接分解质因数肯定血$T$，所以我们每次直接除以$gcd(q,b)$就可以将$q$和$b$共有的质因子除掉，我们这样一直除下去直到$gcd(b,q)=1$或$q=1$时就可以判定了，如果$q=1$输出$Finite$，否则输出$Infinite$。

另外还有一个优化，$b$如果有$q$没有的质因数对结果是不影响的，可以直接将$b$设为$gcd(q,b)$。

代码

#include<bits/stdc++.h>
#define ll long long
using namespace std;
int n;
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
void in(){scanf("%d",&n);}
void ac()
{
    ll p,q,b,g;
    while(n--)
    {
        scanf("%lld%lld%lld",&p,&q,&b);
        for(q/=gcd(p,q),g=gcd(q,b);g!=1&&q!=1;b=g,q/=g,g=gcd(q,b));
        q==1?puts("Finite"):puts("Infinite");
    }
}
int main(){in();ac();}