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.awt.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

public class Main {
    static int mod = (int) 1e9 + 7;
    public static void main(String[] args){
        FastReader sc = new FastReader();
        StringBuilder sb=new StringBuilder();
        int t=sc.nextInt();
        while(t-->0) {
            long a=sc.nextLong(),m=sc.nextLong();
            a=m/gcd(a,m);
            sb.append(eulerT(a)+"\n");
        }
        System.out.println(sb);
    }
    static long gcd(long a,long b){
        if(b==0)return a;
        else return gcd(b,a%b);
    }
    static long eulerT(long m){
        long res=m;
        for(long i=2;i*i<=m;i++){
            if(m%i==0){
                res=res-res/i;
                while(m%i==0)m/=i;
            }
        }
        if(m>1)res-=res/m;
        return res;
    }
}

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;
    }
}