Codeforces Round #483 (Div. 2) C.Finite or not? 关于欧几里得的应用

C. Finite or not?

Input

The first line contains a single integer $\mathrm{nn (1\le n\le 10^5 ) —\; the\; number\; of\; queries.}$

Next $\mathrm{nn lines\; contain\; queries,\; one\; per\; line.\; Each\; line\; contains\; three\; integers p, q and b (0\le p\le 10^18, 1\le q\le 10^18 , 2\le b\le 10^18).\; All\; numbers\; are\; given\; in\; notation\; with\; base 10.}$

Output

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

input

2
6 12 10
4 3 10

output

Finite
Infinite

#include<bits/stdc++.h>
using namespace std;
typedef unsigned long long unsll;

int n;
unsll p,q,b;
unsll gcd(int a,int b)
{
    return b==0? a:gcd(b,a%b);
}

int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0);

    while( cin >> n ){
        while(n--){
            cin >> p >> q >> b;
            if(p%q==0){
                puts("Finite");
                continue;
            }

            unsll cheek=gcd(p,q);
            q/=cheek;
            cheek=gcd(b,q);
            while(q!=1&&cheek!=1){
                while(q%cheek==0) q/=cheek;
                cheek=gcd(b,q);
            }
            if(q==1)
                puts("Finite");
            else puts("Infinite");
        }
    }
    return 0;
}