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 d {

	
	public static void main(String[] args) {
	
		Scanner stdin = new Scanner(System.in);
		int nC = stdin.nextInt();
		
		for (int loop=0; loop<nC; loop++) {
		
			long a = stdin.nextLong();
			long m = stdin.nextLong();
			long div = gcd(a, m);
			//System.out.println("gcd is "+div);
			m /= div;
			System.out.println(phi(m));
		}
	}
	
	public static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a%b);
	}
	
	public static long phi(long n) {
	
		long i = 2, phi = n;
		long saven = n;
		while (i*i <= n) {
		
			int exp = 0;
			while (n%i == 0) {
				exp++;
				n /= i;
			}
			
			if (exp > 0) {
				phi = phi/i*(i-1);
			}
			
			i++;
		}
		
		if (n > 1) phi = phi/n*(n-1);
		return phi;
	}
}