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.*;
import java.util.*;

public class D {
    static long gcd(long a, long b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }
    static long phi(long n)
    {
        // Initialize result as n
        double result = n;

        // Consider all prime factors of n and for
        // every prime factor p, multiply result
        // with (1 - 1/p)
        for (long p = 2; p * p <= n; ++p) {
            // Check if p is a prime factor.
            if (n % p == 0) {
                // If yes, then update n and result
                while (n % p == 0)
                    n /= p;
                result *= (1.0 - (1.0 / (double) p));
            }
        }

        // If n has a prime factor greater than sqrt(n)
        // (There can be at-most one such prime factor)
        if (n > 1)
            result *= (1.0 - (1.0 / (double) n));

        return (long)result;
    }
    static long allDivCount(ArrayList<Long>div,int i,long x,long mul){
        if(i==div.size())return x/mul;
        long tmp = x;
        long res = 0;
        long result = 0;
        while (tmp%div.get(i)==0 && tmp>0){
            //System.out.println("SS");
            tmp/=div.get(i);
            res++;
            result+=allDivCount(div,i+1,x,mul*(long)Math.pow(div.get(i),res));
        }
        return result;
    }
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int q = sc.nextInt();
        while(q-->0){
            long a = sc.nextLong();
            long m = sc.nextLong();
            long c = gcd(a,m);
            a/=c;
            m/=c;
           long res = phi(m);
            pw.println(res);
        }
        pw.flush();
        pw.close();
    }
    static class Pair implements Comparable<Pair>{
        int x;
        int y;
        public Pair(int x,int y){
            this.x= x;
            this.y = y;
        }
        public int compareTo(Pair p){
            return Long.compare(this.y,p.y);
        }

    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();

        }
    }
}