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.


//@author->.....future_me......//
//..............Learning.........//

import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.BigInteger;

public class A {

  // >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Fast IO <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

  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;
    }
  }

  // >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Starts <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //
  static FastReader  sc  = new FastReader();
  static PrintWriter out = new PrintWriter(System.out);

  public static void main(String[] args) throws Exception {
//    try {
//    int t = sc.nextInt();
//    while (t-- > 0)
    A.go();

//    } catch (Exception e) {
//      return;
//    }
  }

  static int mod = 998244353;

  static void go() {
    int n = sc.nextInt();
    while (n-- > 0) {
      long p = sc.nextLong();
      long q = sc.nextLong();
      if (p % q != 0) {

        System.out.println(p);

      } else {
        long xx = q;
        ArrayList<Long> a = new ArrayList<>();
        for (long i = 2; i * i <= xx; i++) {
          if (xx % i == 0) {

            a.add(i);
            while (xx % i == 0) {
              xx /= i;
            }

          }

        }
        if (xx > 1) {
          a.add(xx);
        }
//        for (long i : a) {
//          System.out.print(i + " ");
//        }
        long ans1 = p;
        for (int i = 0; i < a.size(); i++) {
          long x = p;
          long xx1 = q;
          long c = a.get(i);
          ;
          int c1 = 0;
          int c2 = 0;
          while (x % c == 0) {
            x /= c;
            c1++;
          }
          while (xx1 % c == 0) {
            xx1 /= c;
            c2++;
          }
          long val = 1;

          while (c1 >= c2) {
            val *= c;
            c1--;
          }
          ans1 = Math.min(ans1, val);
        }

        out.println(p / ans1);
        out.flush();
      }

    }
  }

  static long gcd(long a, long b) {
    if (b == 0) {
      return a;
    }
    return gcd(b, a % b);
  }

  static int ht[] = new int[100001];

  static void dfs(ArrayList<ArrayList<Integer>> aa, int src, int ht[], boolean vis[]) {
    vis[src] = true;
    ht[src] = 1;
    for (int i : aa.get(src)) {
      if (vis[i] == false) {
        dfs(aa, i, ht, vis);
        ht[src] += ht[i];
      }
    }

  }

  // >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Ends <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

  static void sort(long[] a) {
    ArrayList<Long> aa = new ArrayList<>();
    for (long i : a) {
      aa.add(i);
    }
    Collections.sort(aa);
    for (int i = 0; i < a.length; i++)
      a[i] = aa.get(i);
  }

  static long pow(long x, long y) {
    long res = 1l;
    while (y != 0) {
      if (y % 2 == 1) {
        res = x * res;
      }
      y /= 2;
      x = x * x;
    }
    return res;
  }

}
