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 ≤ n ≤ 10^5) — the number of queries.

Next n lines contain queries, one per line. Each line contains three integers p, q, and b (0 ≤ p ≤ 10^{18}, 1 ≤ q ≤ 10^{18}, 2 ≤ b ≤ 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

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

6/12 = 1/2 = 0,5_{10}

4/3 = 1,(3)_{10}

9/36 = 1/4 = 0,01_2

4/12 = 1/3 = 0,1_3 
import java.util.*;


import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.*;

public class Test4
{
	static class pair
	 {
		Integer x;
		TreeSet<Integer> y;
		pair(int x,TreeSet<Integer> y)
		{
			this.x=x;
			this.y=y;
		}
	}
	static int ans=0;
	static long mod=1000000007;
	static boolean prime[];
	public static long ggcd(long p,long q) {
		if(p<q) {
			long temp = p;
			p=q;
			q=temp;
		}
		while(q!=0) {
			long temp = p;
			p=q;
			q=temp%q;
		}
		return p;
	}
	public static void main(String args[])
	{
		InputReader in=new InputReader(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=in.nextInt();
		while(n--!=0) {
			long p = in.nextLong();
			long q = in.nextLong();
			long b = in.nextLong();
			long bb = b;
			if(p==0 || q==1 || p==q || q==b)
					pw.println("Finite");
			else {
				long g = ggcd(p,q);
				q /=g;
				b = gcd(b,q);
				while(b!=1) {
					while(q%b==0) q /= b;
					b = gcd(b,q);
				}
				if(q==1)
					pw.println("Finite");
				else
					pw.println("Infinite");
			}
		}
//		System.out.println(ggcd(17, Long.parseLong("1000000000000000000")));
		pw.flush();
	}
	public static int distance(int x,int y,int p,int q)
	{
		int a=(x-p)*(x-p);
		int b=(y-q)*(y-q);
		int dis=a+b;
		return dis;
	}
	public static int bnum(int num)
	{
		int ans=0;
		for(int i=31;i>=0;i--)
		{
			if((num&(1<<i))!=0)
			{
				ans+=Math.pow(10,i);
			}
		}
		return ans;
	}
	public static int bsdown(int a[],int item)
	{
		int low=0,high=a.length-1,ans=-1;
		while(low<=high)
		{
			int mid=low+(high-low)/2;
			if(a[mid]<=item)
			{
				ans=mid;
				low=mid+1;
			}
			else
				high=mid-1;
				
		}
		return ans;
	}
	public static long inverse(long num)
	{
		return fastpow(num,mod-2,mod);
	}
	public static int bsupper(int a[],int item)
	{
		int low=0,high=a.length-1,ans=-1;
		while(low<=high)
		{
			int mid=low+(high-low)/2;
			if(a[mid]>=item)
			{
				ans=mid;
				high=mid-1;
			}
			else
				low=mid+1;
				
		}
		return ans;
	}	
	public static boolean isprime(int n)
	{
		for(int i=2;i*i<=n;i++)
		{
			if(n%i==0)
				return false;
		}
		return true;
	}
	public static long fact(long a,long mod)
	{
		long ans=1;
		for(int i=1;i<=a;i++)
		{
			ans*=i;
			ans%=mod;
		}
		return ans%mod;
		
	}
	public static long ncr(long n,long r,long mod)
	{
		long nom=1,dom=1;
		nom=(fact(n,mod))%mod;
		dom=(fact(r,mod)*fact(n-r,mod))%mod;
		return (nom*fastpow(dom,mod-2,mod))%mod;
	}
	public static long gcd(long x, long y)
	{
		if(x==0)
			return y;
		if(y==0)
			return x;
		long r=0, a, b;
		a = (x > y) ? x : y; // a is greater number
		b = (x < y) ? x : y; // b is smaller number
		r = b;
		while(a % b != 0)
		{
			r = a % b;
			a = b;
			b = r;
		}
		return r;
	}
	public static void prime(int n)
	{
		prime[0]=true;
		prime[1]=true;
		for(int i=2;i*i<=n;i++)
		{
			if(prime[i])
				continue;
			for(int j=i;j*i<=n;j++)
			{
				prime[i*j]=true;
			}
		}
	}
	static class InputReader 
	{
		 
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) 
		{
			this.stream = stream;
		}

		public int snext() 
		{
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) 
			{
				curChar = 0;
				try 
				{
					snumChars = stream.read(buf);
				}
				catch (IOException e) 
				{
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt()
		{
			int c = snext();
			while (isSpaceChar(c))
			{
				c = snext();
			}
			int sgn = 1;
			if (c == '-')
			{
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			}
			while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() 
		{
			int c = snext();
			while (isSpaceChar(c)) 
			{
				c = snext();
			}
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			}
			while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) 
		{
			int a[] = new int[n];
			for (int i = 0; i < n; i++) 
			{
				a[i] = nextInt();
			}
			return a;
		}

		public String readString() 
		{
			int c = snext();
			while (isSpaceChar(c)) 
			{
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do
			{
				res.appendCodePoint(c);
				c = snext();
			}
			while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine()
		{
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = snext();
			}
			while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) 
		{
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
	public static long fastpow(long a,long b,long mod)
	{
		long ans=1;
		while(b!=0)
		{
			if(b%2==1)
			{
				ans=(ans*a)%mod;
			}
			a=(a*a)%mod;
			b/=2;
		}
		return ans;
	}
}