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.
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;

public class GFG {
    
    private static long gcd(long a,long b){
        if(a<b)
            return gcd(b,a);
        if(a%b==0)
            return b;
        return gcd(b,a%b);
    }
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine().trim());
		while(t--!=0){
    		String s=br.readLine().trim();
    		String ss[]=s.split("\\s+");
    		long n=Long.parseLong(ss[0]);
    		long m=Long.parseLong(ss[1]);
    		long d=gcd(n,m);
    		m=m/d;
    		long cnt=m;
    		for(int i=2;i<=Math.sqrt(m);i++){
    		    if(m%i==0){
    		        cnt=cnt*(i-1);
    		        cnt/=i;
    		    }
    		    while(m%i==0)
    		        m=m/i;
    		}
    		if(m!=1)
    		    cnt=cnt/m*(m-1);
    		System.out.println(cnt);
		}
	}
}