Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.

To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that: 

  * p_i is divisible by x_i; 
  * x_i is not divisible by q_i. 

Oleg is really good at division and managed to find all the answers quickly, how about you?

Input

The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.

Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.

Output

Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.

One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.

Example

Input


3
10 4
12 6
179 822


Output


10
4
179

Note

For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.

For the second pair, where p_2 = 12 and q_2 = 6, note that 

  * 12 is not a valid x_2, since 12 is divisible by q_2 = 6; 
  * 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6. 

The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
import java.io.*;
import java.util.*;

public class C {
    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;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

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

    static boolean isPrime(int n) {
        //check if n is a multiple of 2
        if (n % 2 == 0) return false;
        //if not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static int MOD=1000000007;



    public static HashMap<Long,Integer> primeFactors(long n)
    {
        // Print the number of 2s that divide n
        HashMap<Long,Integer> map=new HashMap<>();

        while (n % 2 == 0) {
            map.put(2L,map.getOrDefault(2L,0)+1);
            n /= 2;
        }

        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (long i = 3; i <= Math.sqrt(n); i += 2) {
            // While i divides n, print i and divide n
            while (n % i == 0) {
                map.put(i,map.getOrDefault(i,0)+1);
                n /= i;
            }
        }

        // This condition is to handle the case whien
        // n is a prime number greater than 2
        if (n > 2)
            map.put(n,map.getOrDefault(n,0)+1);

        return map;
    }

    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
        int t = ri();
//        int t = 1;
        while (t-- > 0){
            long p=rl();
            long q=rl();
            if(p%q!=0)
            {
                ans.append(p).append("\n");
            }
            else
            {
                HashMap<Long,Integer> map=primeFactors(q);
//                HashMap<Long,Integer> map2=primeFactors(p);
//                System.out.println(map2+" "+p);
//                System.out.println(map);
                long res=1;
                for(long i:map.keySet())
                {
//                    if(map2.containsKey(i))
//                    {
//                        long copy=p;
//                        long val= (long) Math.pow(i,map2.get(i));
//                        copy/=val;
//                        copy *= Math.pow(i, map.get(i) - 1);
//                        res=Math.max(res,copy);
//                    }
//                    else {
//                        res=p;
//                    }
                    long copy=p;
                    while(copy%i==0)
                    {
                        copy/=i;
                    }
//                    for(int j=1;j<map.get(i);j++)
//                    {
//                        copy*=i;
//                    }
//                    if(map.get(i)>1) {
                        copy *=(long) Math.pow(i, map.get(i) - 1);
////                    System.out.println(copy+" "+i);
//
//
//                    }
                    res = Math.max(copy, res);
                }
                assert q%res!=0;
                ans.append(res).append("\n");


            }

        }

        out.print(ans.toString());
        out.flush();

    }
}