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 Quarantine;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class SameGCDs {
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int test=Integer.parseInt(br.readLine());
        StringTokenizer st;
        StringBuilder print=new StringBuilder();
        int seive[]=new int[100001];
        ArrayList<Integer> primes=new ArrayList<>();
        for(int i=2;i<=100000;i++){
            if(seive[i]==0){
                primes.add(i);
                for(int j=2*i;j<=100000;j+=i){
                    seive[j]=1;
                }
            }
        }
        while (test--!=0){
            st=new StringTokenizer(br.readLine());
            long a=Long.parseLong(st.nextToken());
            long m=Long.parseLong(st.nextToken());
            long gcd=gcd(a,m);
            m=m/gcd;
            print.append(getphi(m,primes)+"\n");
        }
        System.out.print(print.toString());
    }
    public static long getphi(long num,ArrayList<Integer> primes){
        long ans=num;
        for(int p:primes){
            if(num==1){
                break;
            }
            if(num%p==0){
                ans=ans-ans/p;
                while (num%p==0){
                    num/=p;
                }
            }
        }
        if(num!=1){
            ans=ans-ans/num;
        }
        return ans;
    }
    public static long gcd(long a,long b){
        if(b==0){
            return a;
        }
        return gcd(b,a%b);
    }
}
