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

Posted 2020-11-05 zquacm-875180305

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

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 typedef unsigned long long unsll;
 4 
 5 int n;
 6 unsll p,q,b;
 7 unsll gcd(int a,int b)
 8 {
 9     return b==0? a:gcd(b,a%b);
10 }
11 
12 int main()
13 {
14     ios_base::sync_with_stdio(0); cin.tie(0);
15 
16     while( cin >> n ){
17         while(n--){
18             cin >> p >> q >> b;
19             if(p%q==0){
20                 puts("Finite");
21                 continue;
22             }
23 
24             unsll cheek=gcd(p,q);
25             q/=cheek;
26             cheek=gcd(b,q);
27             while(q!=1&&cheek!=1){
28                 while(q%cheek==0) q/=cheek;
29                 cheek=gcd(b,q);
30             }
31             if(q==1)
32                 puts("Finite");
33             else puts("Infinite");
34         }
35     }
36     return 0;
37 }