You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).

Note: \gcd(a, b) is the greatest common divisor of a and b.

Input

The first line contains the single integer T (1 ≤ T ≤ 50) — the number of test cases.

Next T lines contain test cases — one per line. Each line contains two integers a and m (1 ≤ a < m ≤ 10^{10}).

Output

Print T integers — one per test case. For each test case print the number of appropriate x-s.

Example

Input


3
4 9
5 10
42 9999999967


Output


6
1
9999999966

Note

In the first test case appropriate x-s are [0, 1, 3, 4, 6, 7].

In the second test case the only appropriate x is 0.

import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
import java.text.*;
public class Rough{     
    
    static PrintWriter w = new PrintWriter(System.out);
    static long mod1=998244353L,mod=1000000007L;
    static long gcd(long a,long b){
        if(b==0){
            return a;
        }
        else{
            return gcd(b,a%b);
        }
    }
    static long lcm(long a,long b){
        return (a*b)/gcd(a,b);
    }
    static long phi(long n) { 
        double result = n; 
        for (long p = 2; p * p <= n; ++p) { 
            if (n % p == 0) { 
                while (n % p == 0) 
                    n /= p; 
                result *= (1.0 - (1.0 / (double)p)); 
            } 
        } 
        if (n > 1) 
            result *= (1.0 - (1.0 / (double)n)); 
  
        return (long)result; 
    } 
    
    public static void main(String args[] ) throws Exception {
        Scanner sc=new Scanner(System.in);
        int q=sc.nextInt();
        while(q-->0){
            long a=sc.nextLong();
            long m=sc.nextLong();
            long g=gcd(a,m);
            w.println(phi(m/g));
            
            
        }
    	w.close();
    }
}