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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class SolutionA extends Thread {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }

    private static final FastReader scanner = new FastReader();
    private static final PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        new Thread(null, new SolutionA(), "Main", 1 << 26).start();
    }

    static class PowerPair {
        long base;
        int exp;

        public PowerPair(long base, int exp) {
            this.base = base;
            this.exp = exp;
        }

        @Override
        public String toString() {
            return base + "^" + exp;
        }
    }

    public static List<PowerPair> getPrimeFactorsOfNumber(long n) {
        List<PowerPair> result = new ArrayList<>();

        for (int i = 2; i <= Math.sqrt(n); i++) {
            PowerPair pair = new PowerPair(i, 0);
            while (n % i == 0) {
                pair.exp++;
                n /= i;
            }

            if (pair.exp > 0) {
                result.add(pair);
            }
        }

        if (n != 1) {
            result.add(new PowerPair(n, 1));
        }

        return result;
    }


    public void run() {
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            solve();
        }
        out.close();
    }

    public static List<Long> getDivisorsOfN(long n) {
        List<Long> result = new ArrayList<>();

        result.add(1L);

        for (int i = 2; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                result.add((long) i);

                if (n / i != i) {
                    result.add(n / i);
                }
            }
        }
        result.add(n);

        return result;
    }

    private static void solve() {
        long p = scanner.nextLong();
        int q = scanner.nextInt();

        List<PowerPair> primeFactors = getPrimeFactorsOfNumber(q);
        if (p < q || p % q != 0) {
            System.out.println(p);
        } else {
            long min = Long.MAX_VALUE;
            for (PowerPair pair: primeFactors) {
                long c = q;
                long amount = 1;
                while (p % c == 0 && amount < min) {
                    if (pair.base > Long.MAX_VALUE / c) {
                        amount *= pair.base;
                        break;
                    } else {
                        c *= pair.base;
                        amount *= pair.base;
                    }
                }
                min = Math.min(min, amount);
            }
            System.out.println(p / min);
        }

    }

    //REMINDERS:
    //- CHECK FOR INTEGER-OVERFLOW BEFORE SUBMITTING

    //- CAN U BRUTEFORCE OVER SOMETHING, TO MAKE IT EASIER TO CALCULATE THE SOLUTION
}