C. Finite or not?+质因子

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 $p$

, $q$ 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 $n$

($1\le n\le {10}^5$

) — the number of queries.

Next $n$

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.

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

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

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

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

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

#define happy

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define all(a) (a).begin(),(a).end()
#define pll pair<ll,ll>
#define vi vector<int>
#define pb push_back
const int inf=0x3f3f3f3f;
ll rd(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}

ll gcd(ll a,ll b){
    if(!b)return a;
    return gcd(b,a%b);
}

bool finite(ll q,ll base){
    while(q!=1){
        ll x=gcd(q,base);
        if(x==1)return false;
        //cout<<x<<endl;
        while(x<numeric_limits<int32_t>::max()/2)x*=x;
        x=gcd(q,x);
        q/=x;
    }
    return true;
}


int main(){
#ifdef happy
    freopen("in.txt","r",stdin);
#endif
    ll n=rd();
    while(n--){
        ll q=rd(),p=rd(),b=rd();
        ll x=gcd(p,q);
        printf("%s\n",finite(p/x,b)?"Finite" : "Infinite");
    }
}