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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author kamol
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class TaskD {
        private long phi(long n) {
            long res = n;
            for (long i = 2; i * i <= n; i++) {
                if ((n % i) == 0) {
                    res -= res / i;
                    while ((n % i) == 0) n /= i;
                }
            }
            if (n != 1) res -= res / n;

            return res;
        }

        long gcd(long a, long b) {
            return (b == 0) ? a : gcd(b, a % b);
        }

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            long x, y;
            x = in.nextLong();
            y = in.nextLong();
            long g = gcd(x, y % x);
            y /= g;
            out.println(phi(y));
        }

    }
}

