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 HelloWorld{

     public static void main(String []args){
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0)
        {
            long a=sc.nextLong();
            long m=sc.nextLong();
            long g=gcd(a,m);
            long x=m/g;
            HashSet<Long> set=new HashSet();
            f(set,x);
            long ans=x;
            Iterator itr=set.iterator();
            while(itr.hasNext())
            {
                long k=(long)itr.next();
                ans=(ans-ans/k);
            }
            System.out.println(ans);
        }
     }
     public static long gcd(long x,long y)
     {
         return y==0?x:gcd(y,x%y);
     }
     public static void f(HashSet<Long> set,long x)
     {
         for(long p=2;p*p<=x;p++)
         {
             if(x%p==0)
             {
                 set.add(p);
                 while(x%p==0)
                 x/=p;
             }
         }
         if(x!=1)
         set.add(x);
     }
}