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.io.*;

public class SameGCDs {
    public static void main(String[] args) throws IOException{
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int t = Integer.parseInt(f.readLine());
        while(t-->0){
            StringTokenizer st = new StringTokenizer(f.readLine());
            long a = Long.parseLong(st.nextToken());
            long b = Long.parseLong(st.nextToken());
            long gcd = gcd(a, b);
            a/=gcd;
            b/=gcd;
            out.println(phi(b));
        }
        out.close();

    }
    public static long gcd(long a, long b){
        while(b != 0){
            long temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }
    public static long phi(long n)
    {
        long result = n;

        for (long p = 2; p * p <= n; ++p)
        {
            if (n % p == 0)
            {
                while (n % p == 0)
                    n /= p;
                result -= result / p;
            }
        }
        if (n > 1)
            result -= result / n;
        return result;
    }
}
