Finite or not?（详细题解）

You are given several queries. Each query consists of three integers $\mathrm{pp, qq and bb.\; You\; need\; to\; answer\; whether\; the\; result\; of p/qp/q in\; notation\; with\; base bb is\; a\; finite\; fraction.}$

A fraction in notation with base $\mathrm{bb is\; finite\; if\; it\; contains\; finite\; number\; of\; numerals\; after\; the\; decimal\; point.\; It\; is\; also\; possible\; that\; a\; fraction\; has\; zero\; numerals\; after\; the\; decimal\; point.}$

Input

The first line contains a single integer $\mathrm{nn (1\le n\le 1051\le n\le 105) —\; the\; number\; of\; queries.}$

Next $\mathrm{nn lines\; contain\; queries,\; one\; per\; line.\; Each\; line\; contains\; three\; integers pp, qq,\; and bb (0\le p\le 10180\le p\le 1018, 1\le q\le 10181\le q\le 1018, 2\le b\le 10182\le b\le 1018).\; All\; numbers\; are\; given\; in\; notation\; with\; base 1010.}$

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

$\frac{\mathrm{612=12=0,510612=12=0,510}}{}$

$\frac{\mathrm{43=1,(3)1043=1,(3)10}}{}$

$\frac{\mathrm{936=14=0,012936=14=0,012}}{}$

$\frac{\mathrm{412=13=0,13}}{}$

#include <iostream>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int main()
{
    int n;
    scanf("%d",&n);
    while(n--)
    {
        ll p,q,b;
        scanf("%I64d%I64d%I64d",&p,&q,&b);
        ll g=__gcd(p,q);
        p/=g;
        q/=g;
        if(q==1||p==0)
        {
            printf("Finite
");
        }
        else
        {
            while(q!=1&&b!=1)
            {
                b=__gcd(b,q);
                q/=b;
            }
            if(q==1)
            {
                printf("Finite
");
            }
            else
            {
                printf("Infinite
");
            }
        }
    }
    return 0;
}