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,qp,qp, q and bbb. You need to answer whether the result of p/q" role="presentation" style="position: relative;">p/qp/qp/q in notation with base bbb is a finite fraction.

A fraction in notation with base b" role="presentation" style="position: relative;">bbb 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≤105)n(1≤n≤105)n (1≤n≤10^5) — the number of queries.

Next nnn lines contain queries, one per line. Each line contains three integers p,q" role="presentation" style="position: relative;">p,qp,qp, q, and b(0≤p≤1018,1≤q≤1018,2≤b≤1018)b(0≤p≤1018,1≤q≤1018,2≤b≤1018)b (0≤p≤10^{18},1≤q≤10^{18}, 2≤b≤10^{18}). All numbers are given in notation with base 101010.

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

612=12=0,510612=12=0,510\frac{6}{12}=\frac{1}{2}=0,5_{10}

43=1,(3)1043=1,(3)10\frac{4}{3}=1,(3)_{10}

936=14=0,012936=14=0,012\frac{9}{36}=\frac{1}{4}=0,01_2

412=13=0,13412=13=0,13\frac{4}{12}=\frac{1}{3}=0,1_3

题解

先约一波分，如果qqq的质因数都是b" role="presentation" style="position: relative;">bbb的因数，那么pqpq\frac{p}{q}在bbb进制下就是有限的。

但是值域是1018" role="presentation" style="position: relative;">1018101810^{18}，直接分解质因数肯定血TTT，所以我们每次直接除以gcd(q,b)" role="presentation" style="position: relative;">gcd(q,b)gcd(q,b)gcd(q,b)就可以将qqq和b" role="presentation" style="position: relative;">bbb共有的质因子除掉，我们这样一直除下去直到gcd(b,q)=1gcd(b,q)=1gcd(b,q)=1或q=1q=1q=1时就可以判定了，如果q=1q=1q=1输出FiniteFiniteFinite，否则输出InfiniteInfiniteInfinite。

另外还有一个优化，bbb如果有q" role="presentation" style="position: relative;">qqq没有的质因数对结果是不影响的，可以直接将bbb设为gcd(q,b)" role="presentation" style="position: relative;">gcd(q,b)gcd(q,b)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();}