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 final class D1295 {

    private static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    private static long phi(long n) {
        long answer = n;
        for (long i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                while (n % i == 0) {
                    n /= i;
                }
                answer -= answer / i;
            }
        }
        if (n > 1) answer -= answer / n;
        return answer;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while (t-- > 0) {
            long a = in.nextLong();
            long m = in.nextLong();
            System.out.println(phi(m / gcd(a, m)));
        }
    }
}
