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 Solution
{
     static class Pair{
        int parent;
        int rank;
        Pair(int parent,int rank)
        {
            this.rank=rank;
            this.parent=parent;
        }
    }
    static int find(Pair pr[],int i)
    {
        if(i==pr[i].parent)
            return i;
        else
        {
            pr[i].parent=find(pr,pr[i].parent);
            return pr[i].parent;
        }
    }
    static void join(Pair[] pr,int i,int j)
    {
        i=find(pr,i);
        j=find(pr,j);
        if(i==j)
            return;
        if(pr[i].rank>=pr[j].rank)
        {
            pr[j].parent=i;
            pr[i].rank+=pr[j].rank;
        }
        else
        {
            pr[i].parent = j;
            pr[j].rank+=pr[i].rank;
        }
    }
    static void swap(char ar[],int i,int j)
    {
        char f = ar[i];
        ar[i]=ar[j];
        ar[j]=f;
    }
    static ArrayList<Integer> graph[] ;
    static long mul[][];
    public static void main (String[] args) throws IOException
    {
        StringBuilder sb = new StringBuilder();
        FastReader s1 = new FastReader();
        int t=s1.I();
        while(t--!=0)
        {
            long a =s1.L();
            long m=s1.L();
            long temp=gcd(a,m);
            long n=m/temp;
            sb.append(phi(n)).append("\n");
        }
        System.out.println(sb);
    }
    static long phi(long n)
    {
        long result=n;
        for(int i=2;i<=Math.sqrt(n);i++)
        {
            if(n%i==0)
            {
                result-=result/i;
            }
            while(n%i==0)
            {
                n=n/i;
            }
        }
        if(n>1)
        {
            result-=(result/n);
        }
        return result;
    }
    static ArrayList<Integer> primeFactor(int n)
    {
        ArrayList<Integer> ans = new ArrayList<>();
        if(n%2==0)
            ans.add(2);
        while (n%2==0)
        {   
            n /= 2;
        }
        for (int i = 3; i <= Math.sqrt(n); i+= 2)
        {
            if(n%i==0)
                ans.add(i);
            while (n%i == 0)
            {
                n /= i;
            }
        }
        if (n > 2)
            ans.add(n);
        return ans;
    }
    static int longestSubSeg(int a[], int n,int k)
    {
        int cnt0 = 0;
        int l = 0;
        int max_len = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] == 0)
                cnt0++;
            while (cnt0 > k) {
                if (a[l] == 0)
                    cnt0--;
                l++;
            }
            max_len = Math.max(max_len, i - l + 1);
        }
        
        return max_len;
    }
    static void dfs(int index,boolean ar[])
    {
        ar[index]=true;
        for(int i=0;i<graph[index].size();i++)
        {
            if(!ar[graph[index].get(i)])
            {
                dfs(graph[index].get(i),ar);
            }
        }
    }
    static int binary(int left,int right,int ar[],int no)
    {
        int mid=(left+right)/2;
        if(Math.abs(right-left)<=1)
        {
            if(no>=ar[right])
            {
                return right+1;
            }
            else if(no<ar[left])
            {
                return left;
            }
            else
            {
                return left+1;
            }
        }
        if(ar[mid]>no)
        {
            right=mid-1;
            return binary(left, right, ar, no);
        }
        else{
            left=mid;
            return binary(left, right, ar, no);
        }
    }
    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 I()
        {
            return Integer.parseInt(next());
        }
        
        long L()
        {
            return Long.parseLong(next());
        }
        
        double D()
        {
            return Double.parseDouble(next());
        }
        
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
    static long gcd(long a,long b)
    {
        if(a%b==0)
            return b;
        return gcd(b,a%b);
    }
    static float power(float x, int y)
    {
        float temp;
        if( y == 0)
            return 1;
        temp = power(x, y/2);
        
        if (y%2 == 0)
            return temp*temp;
        else
        {
            if(y > 0)
                return x * temp * temp;
            else
                return (temp * temp) / x;
        }
    }
    static long pow(long x, long y)
    {
        int p = 1000000007;
        long res = 1;
        x = x % p;
        while (y > 0)
        {
            if((y & 1)==1)
                res = (res * x) % p;
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }
    static ArrayList<Integer> sieveOfEratosthenes(int n)
    {
        ArrayList<Integer> arr=new ArrayList<Integer>();
        boolean prime[] = new boolean[n+1];
        for(int i=2;i<n;i++)
            prime[i] = true;
        
        for(int p = 2; p*p <=n; p++)
        {
            if(prime[p] == true)
            {
                arr.add(p);
                for(int i = p*p; i <= n; i += p)
                    prime[i] = false;
            }
        }
        return arr;
    }
}
