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.*;

public class CF102 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
      //  long modulo=10;
        int t=sc.nextInt();
        for (int i=1;i<=t;i++){
            long a=sc.nextLong();
            long m=sc.nextLong();
            long gcd=gcd(a,m);
           long m_dash=m/gcd;
            System.out.println(totient(m_dash));
        }

    }

    public static long power(long a,long b,long c){
        long ans=1;
        while (b!=0){
            if (b%2==1){
                ans=ans*a;
                ans%=c;
            }
            a=a*a;
            a%=c;
            b/=2;
        }
        return ans;
    }
    public static long power1(long a,long b,long c){
        long ans=1;
        while (b!=0){
            if(b%2==1){
                ans=multiply(ans,a,c);
            }
            a=multiply(a,a,c);
            b/=2;

        }
        return ans;

    }

    public static long multiply(long a,long b,long c){
        long res=0;
        a%=c;
        while (b>0){
            if(b%2==1){
               res=(res+a)%c;
            }
            a=(a+a)%c;
            b/=2;
        }

        return res%c;

    }
     public static long totient(long n){
        long result=n;
        for(long i=2;i*i<=n;i++){
            if(n%i==0){
                while (n%i==0){
                    n/=i;
                }
                result-=result/i;
            }
        }
        if (n>1){
            result-=result/n;
        }
        return result;
     }



    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }
}
