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.BufferedOutputStream;
import java.io.BufferedReader;
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 {
    //--------------------------------------------------------
    private static final MyScanner in = new MyScanner(System.in);
    private static final PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    public static void main(String[] args) throws Exception {
        Solver solver = new Solver();
        solver.solve();
        out.close();
    }

    private static class Solver {
        private int MAX = 100_000;
        private int[] prime = new int[MAX];
        private int totalPrime = 0;
        private int[] check = new int[MAX];

        private void solve() throws Exception {
            int t = in.nextInt();

            for (int i = 2; i < MAX; ++i) {
                if (check[i] == 0) {
                    prime[totalPrime++] = i;
                }
                for (int j = 0; j < totalPrime; ++j) {
                    if (i * prime[j] >= MAX) {
                        break;
                    }
                    check[i * prime[j]] = 1;
                    if (i % prime[j] == 0) {
                        break;
                    }
                }
            }

            while (t-- > 0) {
                long a = in.nextLong();
                long b = in.nextLong();
                if (a % b != 0) {
                    out.println(a);
                } else {
                    out.println(compute(a, b));
                }
            }
        }

        private long compute(long a, long b) {
            List<Long[]> parts = new ArrayList<>();
            long bp = b;
            for (int i = 0; i < totalPrime; i++) {
                long n = 0;

                while (bp % prime[i] == 0) {
                    n++;
                    bp /= prime[i];
                }
                if (n > 0) {
                    parts.add(new Long[]{(long) prime[i], n});
                }
            }
            if (bp > 1) {
                parts.add(new Long[]{bp, 1L});
            }

            long ans = 0;
            for (Long[] p : parts) {
                long ap = a;
                while (ap % p[0] == 0) {
                    ap /= p[0];
                }
                for (int i = 1; i < p[1]; i++) {
                    ap *= p[0];
                }
                ans = Math.max(ap, ans);
            }
            return ans;
        }
    }

    public static class MyScanner {
        private final BufferedReader br;
        private StringTokenizer st;

        public MyScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreElements()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

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

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

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

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