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.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class C {
    FastScanner scanner;
    PrintWriter writer;

    void solve() throws IOException {
        scanner = new FastScanner(System.in);
        writer = new PrintWriter(System.out);

        int tests = scanner.nextInt();

        for (int test = 0; test < tests; test++) {
            long p = scanner.nextLong();
            int q = scanner.nextInt();

            writer.println(findMaxRefinedDivisor(p, q));
        }

        writer.close();
    }

    long findMaxRefinedDivisor(long p, int q) {
        List<Integer> divisors = findPrimeDivisors(q);

        long ans = 0;

        for (int d : divisors) {
            long x = p;
            while (x % q == 0)
                x = x / d;
            ans = Math.max(ans, x);
        }

        return ans;
    }

    private List<Integer> findPrimeDivisors(int q) {
        List<Integer> divisors = new ArrayList<>();
        for (int k = 2; (long) k * k <= q; k++) {
            if (q % k == 0)
                divisors.add(k);
            while (q % k == 0) {
                q /= k;
            }
        }

        if (q != 1)
            divisors.add(q);

        return divisors;
    }

    public static void main(String[] args) throws IOException {
        new C().solve();
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer tokenizer;

        FastScanner(InputStream is) {
            this.br = new BufferedReader(new InputStreamReader(is));
        }

        FastScanner(File file) throws FileNotFoundException {
            this(new FileInputStream(file));
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        String next() throws IOException {
            while (tokenizer == null || !tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(br.readLine());

            return tokenizer.nextToken();
        }

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

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