#include <bits/stdc++.h>
using namespace std;
int32_t main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n, m;
    cin >> n >> m;
    if (n % m != 0) {
      cout << n << endl;
      continue;
    } else {
      long long l = -1;
      vector<long long> v;
      v.push_back(m);
      for (long long i = 2; i * i <= m; i++) {
        if (m % i == 0) {
          if (m / i == i) {
            v.push_back(i);
          } else {
            v.push_back(m / i);
            v.push_back(i);
          }
        }
      }
      long long ans = 0;
      for (long long i = 0; i < v.size(); i++) {
        if (n % v[i] == 0) {
          long long temp = n;
          while (temp % v[i] == 0) {
            temp = temp / v[i];
            if (temp % m != 0) {
              ans = max(ans, temp);
              break;
            }
          }
        }
      }
      cout << ans << endl;
    }
  }
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int32_t main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n, m;
    cin >> n >> m;
    if (n % m != 0) {
      cout << n << endl;
      continue;
    } else {
      long long l = -1;
      vector<long long> v;
      v.push_back(m);
      for (long long i = 2; i * i <= m; i++) {
        if (m % i == 0) {
          if (m / i == i) {
            v.push_back(i);
          } else {
            v.push_back(m / i);
            v.push_back(i);
          }
        }
      }
      long long ans = 0;
      for (long long i = 0; i < v.size(); i++) {
        if (n % v[i] == 0) {
          long long temp = n;
          while (temp % v[i] == 0) {
            temp = temp / v[i];
            if (temp % m != 0) {
              ans = max(ans, temp);
              break;
            }
          }
        }
      }
      cout << ans << endl;
    }
  }
}

```