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.
//package round_680_div2;

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

public class QuestionC {

    public static void main(String[] args){
        out = new PrintWriter(new BufferedOutputStream(System.out));
        in = new MyScanner();
        int t = in.nextInt();
        while (t-- > 0)
            System.out.println(solve(in.nextLong(), in.nextLong()));
        out.close();
    }

    private static long factor(long v, long f) {
        long cnt = 0;
        while (true) {
            if (v % f == 0) {
                cnt++;
                v /= f;
            } else {
                break;
            }
        }
        return cnt;
    }

    public static long solve(long p, long q) {
        if (p < q) {
            return p;
        }
        if (p % q != 0) {
            return p;
        }

        long P = p;
        long Q = q;
        long best = P;

        long qf2 = factor(q, 2);
        long pf2 = factor(p, 2);
        Q /= power(2, qf2);
        P /= power(2, pf2);
        if (qf2 > 0 && pf2 > 0) {
            long sacr = (power(2, pf2 - qf2 + 1));
//            System.out.println(2 + " " + pf2 + " " + qf2 + " " + sacr);
            best = Math.min(best, sacr);
        }

        for (long i=3; i <= Math.sqrt(q); i = i + 2) {
            long pf = factor(P, i);
            P /= power(i, pf);

            long qf = factor(Q, i);
            Q /= power(i, qf);

            if (qf > 0 && pf > 0) {
                long sacr = (power(i, pf - qf + 1));
//                System.out.println(i + " " + pf + " " + qf + " " + sacr);
                best = Math.min(best, sacr);
            }
        }

        if (Q > 2) {
            long pf = factor(P, Q);
            if (pf > 0) {
                long sacr = (power(Q, pf));
//                System.out.println(q + " " + pf + " " + qf + " " + sacr);
                best = Math.min(best, sacr);
            }
        }
        return p / best;
    }


    static long power(long a, long b) {
        long power = 1;
        for(long c = 0; c < b; c++)
            power *= a;
        return power;
    }

    public static PrintWriter out;
    public static MyScanner in;
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }

        List<Integer[]> readListOfIntsHorizontal(int n, int m) {
            List<Integer[]> ret = new ArrayList<>();
            for (int j=0; j<n; j++){
                ret.add(new Integer[m]);
            }
            for (int i=0; i<n; i++) {
                for(int j=0; j<m; j++) {
                    ret.get(i)[j] = nextInt();
                }
            }
            return ret;
        }

        List<Integer[]> readListOfIntsVertical(int n, int m) {
            List<Integer[]> ret = new ArrayList<>();
            for (int j=0; j<m; j++){
                ret.add(new Integer[n]);
            }
            for (int i=0; i<n; i++) {
                for(int j=0; j<m; j++) {
                    ret.get(j)[i] = nextInt();
                }
            }
            return ret;
        }
    }
}