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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Random;
import java.util.StringTokenizer;

public class Solution{
	
	static ArrayList<Long> primes;
	
	

	public static void main(String[] args) {

		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		
		
		int tt = fs.nextInt();
		while(tt-->0) {
			
			long a = fs.nextLong(), b = fs.nextLong();
			long g = gcd(a, b);
			
			out.println(phi(b/g));
			
			
			
			
			
			
			
			
			
		}
		
		out.close();
		
	}
	
	//TOTIENT FUNCTION
	static long phi(long n) {
		long res = n;
		for(int i=2;(long)i*i<=n;i++) {
			if(n%i==0) {
				res -= res/i;
				while(n%i==0) n = n/i;
			}
		}
		if(n>1) res -= res/n;
		return res;
	}
	
	
	
	
	static long gcd(long a, long b) {
		if(b==0) return a;
		return gcd(b, a%b);
	}
	
	
	
	
	static final Random random=new Random();
	
	static void ruffleSort(int[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n), temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	
	
	
	static class FastScanner{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		public String next(){
			while(!st.hasMoreElements()){
				try{
					st = new StringTokenizer(br.readLine());
				} catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		public String nextLine() throws IOException {
			return br.readLine();
		}
		
		public int nextInt(){
			return Integer.parseInt(next());
		}

		public int[] readArray(int n){
			int[] a = new int[n];
			for(int i=0;i<n;i++)
				a[i] = nextInt();
			return a;
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public char nextChar() {
			return next().toCharArray()[0];
		}
	}
	
}
