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 main;
import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.*;
public class Submission {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter (System.out);
        //BufferedReader reader = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt")));
        //StringTokenizer st = new StringTokenizer(reader.readLine()," ");
        int T = Integer.parseInt(reader.readLine());
        for (int i=0;i<T;i++) {
        	StringTokenizer st = new StringTokenizer(reader.readLine()," ");
        	BigInteger a = new BigInteger(st.nextToken());
        	BigInteger m = new BigInteger(st.nextToken());
        	BigInteger gcd = a.gcd(m);
        	a = a.divide(gcd);
        	m = m.divide(gcd);
        	long newm = Long.parseLong(m.toString());
        	//out.print(newm+" ");
        	int[] primecount = new int[100001];
        	for (long x=2;x<=100000;x++) {
        		while (newm%x==0) {
        			newm=newm/x;
        			primecount[(int)x]++;
        		}
        	}
        	long answer=1;
        	if (newm>1) answer=newm-1;
        	for (int x=2;x<100001;x++) {
        		if (primecount[x]>0) answer=answer*(x-1);
        		if (primecount[x]>1) for (int j=0;j<primecount[x]-1;j++) answer=answer*x;
        	}
        	out.println(answer);
        }
        reader.close();
        out.close();
    }
}