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.
/*
 *created by Kraken on 30-04-2020 at 14:56
 */
//package com.kraken.cf.practice;

import java.util.*;
import java.io.*;

public class D1295 {

  public static void main(String[] args) {
    FastReader sc = new FastReader();
    int t = sc.nextInt();
    StringBuilder sb = new StringBuilder();
    while (t-- > 0) {
      long a = sc.nextLong(), m = sc.nextLong();
      sb.append(phi(m / gcd(a, m))).append("\n");
    }
    System.out.print(sb);
  }

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

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

  static class FastReader {

    BufferedReader br;

    StringTokenizer st;

    public FastReader() {
      br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        }
        catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

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

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

    double nextDouble() {
      return Double.parseDouble(next());
    }

    String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      }
      catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }
  }
}
