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.Scanner;
//欧拉总函数的定义
public class Main{
	public static long gcd(long a,long b) {
		return a==0?b:gcd(b%a,a);
	}
	public static long phi(long a) {
		long d=2l;
		long ans=a;
		long tmp=a;
		while(d*d<=tmp) {
			long cnt=0;
			while(tmp%d==0l) {
				tmp/=d;
				cnt++;
			}
			if(cnt>0) {
				ans-=ans/d;
			}
			d++;
		}
		if(tmp>1l) {
			ans-=ans/tmp;
		}
		return ans;
	}
	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();
			System.out.println(phi(m/gcd(a,m)));
		}
	}
}