#include <bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(char c) {
  string s;
  s += c;
  return s;
}
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "1" : "0"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (long long i = 0; i < static_cast<long long>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
void Clearing_out() { return; }
template <typename Head, typename... Tail>
void Clearing_out(Head& H, Tail&... T) {
  H.clear();
  Clearing_out(T...);
}
void testcase() {
  long long p, q;
  cin >> p >> q;
  if (p % q) {
    cout << p << '\n';
  } else {
    vector<pair<long long, long long>> lol;
    long long x = q;
    for (long long i = 2; i * i <= x; i++) {
      long long cnt = 0;
      while (x % i == 0) {
        cnt++;
        x /= i;
      }
      if (cnt > 0) lol.push_back({i, cnt});
    }
    long long ans = p;
    long long temp = p;
    if (x != 1) lol.push_back({x, 1});
    for (auto [pr, f] : lol) {
      long long cnt = 0;
      while (temp % pr == 0) temp /= pr, cnt++;
      long long extra = max(0ll, cnt - f + 1);
      long long c = 1;
      for (long long i = 0; i < extra; i++) {
        c *= pr;
      }
      ans = min(ans, c);
    }
    cout << p / ans << '\n';
  }
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long tt = 1;
  cin >> tt;
  while (tt--) {
    testcase();
  }
  return 0;
}

### 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;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(char c) {
  string s;
  s += c;
  return s;
}
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "1" : "0"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (long long i = 0; i < static_cast<long long>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
void Clearing_out() { return; }
template <typename Head, typename... Tail>
void Clearing_out(Head& H, Tail&... T) {
  H.clear();
  Clearing_out(T...);
}
void testcase() {
  long long p, q;
  cin >> p >> q;
  if (p % q) {
    cout << p << '\n';
  } else {
    vector<pair<long long, long long>> lol;
    long long x = q;
    for (long long i = 2; i * i <= x; i++) {
      long long cnt = 0;
      while (x % i == 0) {
        cnt++;
        x /= i;
      }
      if (cnt > 0) lol.push_back({i, cnt});
    }
    long long ans = p;
    long long temp = p;
    if (x != 1) lol.push_back({x, 1});
    for (auto [pr, f] : lol) {
      long long cnt = 0;
      while (temp % pr == 0) temp /= pr, cnt++;
      long long extra = max(0ll, cnt - f + 1);
      long long c = 1;
      for (long long i = 0; i < extra; i++) {
        c *= pr;
      }
      ans = min(ans, c);
    }
    cout << p / ans << '\n';
  }
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long tt = 1;
  cin >> tt;
  while (tt--) {
    testcase();
  }
  return 0;
}

```