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;
int t, i;
int c[32650];
void ciu();
unsigned long long int p, q;
unsigned long long int minim = 0xffffffffffffffff;
vector<unsigned long long int> v;
int main() {
  cin >> t;
  ciu();
  while (t--) {
    minim = 0xffffffffffffffff;
    cin >> p >> q;
    if (p % q != 0)
      cout << p << '\n';
    else {
      for (i = 0; i < v.size() && v[i] * v[i] <= q; i++)
        if (q % v[i] == 0) {
          unsigned long long int exp = 0, rez = 1;
          while (q % v[i] == 0) {
            q /= v[i];
            exp++;
            rez *= v[i];
          }
          if (rez != 1) {
            unsigned long long int expx = 0, rezx = 1;
            unsigned long long int cp = p;
            cp /= rez;
            while (cp % v[i] == 0) {
              cp /= v[i];
              expx++;
              rezx *= v[i];
            }
            rezx *= v[i];
            if (rezx < minim) minim = rezx;
          }
        }
      if (q != 1) {
        unsigned long long int expq = 0, rezq = 1;
        unsigned long long int cp = p;
        cp /= q;
        while (cp % q == 0) {
          cp /= q;
          expq++;
          rezq *= q;
        }
        rezq *= q;
        if (rezq < minim) minim = rezq;
      }
      cout << p / minim << '\n';
    }
  }
  return 0;
}
void ciu() {
  int i, j;
  for (i = 2; i * i < 32650; i++)
    if (!c[i])
      for (j = i * i; j < 32650; j += i) c[j] = 1;
  for (i = 2; i < 32650; i++)
    if (!c[i]) v.push_back(i);
}
