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 Solution {
    public static void main(String []args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int not = Integer.parseInt(br.readLine());
        while(not--!=0) {
            String input[] = br.readLine().split(" ");
            long a = Long.parseLong(input[0]);
            long m = Long.parseLong(input[1]);
            long x = gcd(a, m);
            long n = m / x;

            double result = n; 

            if(n % 2 == 0) {
                while(n % 2 == 0) {
                    n /= 2;
                }
                result *= (1.0 - (1.0 / (double)2));
            }
            for (long p = 3; p * p <= n; p += 2) {
                if (n % p == 0) {
                    while (n % p == 0)
                        n /= p;
                    result *= (1.0 - (1.0 / (double)p));
                }
            }
            if (n > 1)
                result *= (1.0 - (1.0 / (double) n));
            System.out.println((long)result);
        }
    }
    static long gcd(long a, Long m) {
        if(m % a == 0) return a;
        return gcd(m%a, a);
    }
}