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.io.*;
public class same_gcd {
    static long gcd(long a,long b){
        if(a==0)return b;
        return gcd(b%a,a);
    }
    static long fun_phi(long n){
        long flag=2L;
        long temp=n;
        long result=n;
        while(flag*flag<=temp){
            int count=0;
            while(n%flag==0){
                n/=flag;
                count++;
            }
            if(count>0){
                result-=result/flag;
            }
            flag++;
        }
        if(n>1L)result-=result/n;
        return result;
    }
    public static void main(String []args) throws IOException {
        BufferedReader br =  new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        while(t-->0){
            String st = br.readLine();
            String []temp = st.split(" ");
            long a = Long.parseLong(temp[0]);
            long m = Long.parseLong(temp[1]);
            long _gcd=gcd(a,m);
            System.out.println(fun_phi(m/_gcd));
        }
    }
}
