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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeMap;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author xwchen
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int testCase = in.nextInt();
            while (testCase-- > 0) {
                long p = in.nextLong();
                long q = in.nextLong();
                if (p % q != 0) {
                    out.println(p);
                    continue;
                }
                Map<Long, Integer> primes = MathUtil.getPrimeDivisors(q);
                long best = 1;
                for (Map.Entry<Long, Integer> prime : primes.entrySet()) {
                    long y = p;
                    long z = 1;
                    for (int i = 0; i < prime.getValue() - 1; ++i) {
                        z *= prime.getKey();
                    }
                    while (y % prime.getKey() == 0) {
                        y /= prime.getKey();
                    }
                    y *= z;
                    best = Math.max(best, y);
                }
                out.println(best);
            }
        }

    }

    static class MathUtil {
        public static TreeMap<Long, Integer> getPrimeDivisors(long n) {
            TreeMap<Long, Integer> r = new TreeMap<>();
            for (long i = 2; i * i <= n; ++i) {
                if (n % i == 0) {
                    r.put(i, 0);
                    int cnt = 0;
                    while (n % i == 0) {
                        ++cnt;
                        n /= i;
                    }
                    r.put(i, cnt);
                }
            }
            if (n > 1) {
                r.put(n, 1);
            }
            return r;
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public InputReader(InputStream inputStream) {
            this.reader = new BufferedReader(
                    new InputStreamReader(inputStream));
        }

        public String next() {
            while (!tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

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

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

    }
}

