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.*;

/**
 * Created by Katushka on 11.03.2020.
 */
public class Main {

    static int[] readArray(int size, InputReader in) {
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }

    static long[] readLongArray(int size, InputReader in) {
        long[] a = new long[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextLong();
        }
        return a;
    }

    static List<long[]> primeDivisors(long n) {
        long d = 2;
        List<long[]> res = new ArrayList<>();
        while (d * d <= n) {
            if (n % d == 0) {
                long[] p = {d, 1};
                res.add(p);
                while (n % d == 0) {
                    p[1] *= d;
                    n /= d;
                }
            } else {
                d += 1;
            }
        }
        if (n > 1) {
            res.add(new long[]{n, n});
        }
        return res;
    }

    private static long maxDivisor(long n) {
        long d = 2;
        long res = 1;
        while (d * d <= n) {
            if (n % d == 0) {
                res = Math.max(res, n / d);
                res = Math.max(res, d);
            }
            d += 1;
        }
        return res;
    }

    public static void main(String[] args) throws FileNotFoundException {
//        InputReader in = new InputReader(new FileInputStream("gangs.in"));
//        PrintWriter out = new PrintWriter(new BufferedOutputStream(new FileOutputStream("gangs.out")));

        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        int qs = in.nextInt();
        for (int t = 0; t < qs; t++) {
            long p = in.nextLong();
            long q = in.nextLong();

            if (p < q) {
                out.println(p);
            } else if (p == q) {
                out.println(maxDivisor(p));
            } else if (p % q != 0) {
                out.println(p);
            } else {
                List<long[]> primes = primeDivisors(q);

                long maxX = 1;
                for (int i = 0; i < primes.size(); i++) {
                    long[] d = primes.get(i);
                    long b = p / d[1];
                    while (b % d[0] == 0) {
                        b /= d[0];
                    }
                    maxX = Math.max(maxX, (d[1] / d[0]) * b);

                }
                out.println(maxX);
            }

        }


        out.close();
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                createTokenizer();
            }
            return tokenizer.nextToken();
        }

        private void createTokenizer() {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public String nextWord() {
            return next();
        }

        public String nextString() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public char nextChar() {
            return next().charAt(0);
        }

        public int[] nextInts() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                createTokenizer();
            }
            List<Integer> res = new ArrayList<>();
            while (tokenizer.hasMoreElements()) {
                res.add(Integer.parseInt(tokenizer.nextToken()));
            }
            int[] resArray = new int[res.size()];
            for (int i = 0; i < res.size(); i++) {
                resArray[i] = res.get(i);
            }
            return resArray;
        }
    }
}