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.*;
import java.lang.*;

public class SameGcd {

	public static void main(String[] args) {
		Scanner scn =new Scanner(System.in);
		int t=scn.nextInt();
		while(t-- !=0) {
			long a=scn.nextLong();
			long m=scn.nextLong();
			long g=gcd(a,m);
			System.out.println(findNum(m/g));
		}
	}
	public static long findNum(long l) {
		long ans=l;
		for(long i=2;i*i<=l;i++) {
			if(l%i==0) {
				ans-=ans/i;
				while(l%i==0)
					l=l/i;
			}
		}
		if(l>1)
			ans-=ans/l;
		return ans;
	}
public static long gcd(long a,long b) {
	if(a==0)
		return b;
	return gcd(b%a,a);
}
}
