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;
using ll = long long;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long>>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using u32 = uint32_t;
using u64 = uint64_t;
template <typename T>
void re(T &x);
template <typename T>
void re(vector<T> &v);
template <typename T, typename... Q>
void re(T &x, Q &...y);
template <typename T>
void re(T &x) {
  cin >> x;
}
template <typename T>
void re(vector<T> &v) {
  for (auto &x : v) re(x);
}
template <typename T, typename... Q>
void re(T &x, Q &...y) {
  re(x);
  re(y...);
}
namespace number_theory {
template <typename T>
std::vector<std::pair<T, int>> factor(T x) {
  if (x <= 1) return {};
  std::vector<std::pair<T, int>> pr;
  for (T i = 2; i * i <= x; ++i) {
    if (x % i == 0) {
      int n = 0;
      while (x % i == 0) x /= i, ++n;
      pr.push_back({i, n});
    }
  }
  if (x > 1) pr.push_back({x, 1});
  return pr;
}
ll phi(ll x) {
  for (auto &i : factor(x)) x -= x / i.first;
  return x;
}
}  // namespace number_theory
ll solve(ll p, ll q) {
  if (p % q != 0) {
    return p;
  } else {
    ll ans = 1;
    for (auto &f : number_theory::factor(q)) {
      ll P = p;
      for (P = p; P % q == 0;) P /= f.first;
      ans = max(ans, P);
    }
    return ans;
  }
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    ll p, q;
    cin >> p >> q;
    cout << solve(p, q) << '\n';
  }
}
