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.
#include <bits/stdc++.h>
using namespace std;
long long read() {
  long long num1 = 0, zfh = 1;
  char c;
  c = getchar();
  while (!isdigit(c)) {
    if (c == '-') zfh = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    num1 = num1 * 10 + c - '0';
    c = getchar();
  }
  return num1 * zfh;
}
long long t, p, q, ans;
int main() {
  t = read();
  while (t--) {
    ans = 0;
    p = read();
    q = read();
    if (p % q != 0 || p < q) {
      printf("%lld\n", p);
      continue;
    }
    for (long long i = 2; i * i <= q; i++) {
      if (q % i != 0) {
        continue;
      }
      long long temp1 = p, temp2 = p, other = q / i;
      while (temp1 % q == 0) temp1 /= i;
      while (temp2 % q == 0) temp2 /= other;
      ans = max(max(temp1, temp2), ans);
    }
    long long temp = p;
    while (temp % q == 0) temp /= q;
    ans = max(ans, temp);
    printf("%lld\n", ans);
  }
  return 0;
}
