Problem: Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.

A common divisor for two positive numbers is a number which both numbers are divisible by.

But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor d between two integers a and b that is in a given range from low to high (inclusive), i.e. low ≤ d ≤ high. It is possible that there is no common divisor in the given range.

You will be given the two integers a and b, then n queries. Each query is a range from low to high and you have to answer each query.

Input

The first line contains two integers a and b, the two integers as described above (1 ≤ a, b ≤ 109). The second line contains one integer n, the number of queries (1 ≤ n ≤ 104). Then n lines follow, each line contains one query consisting of two integers, low and high (1 ≤ low ≤ high ≤ 109).

Output

Print n lines. The i-th of them should contain the result of the i-th query in the input. If there is no common divisor in the given range for any query, you should print -1 as a result for this query.

Examples

Input

9 27
3
1 5
10 11
9 11


Output

3
-1
9

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<int> fac;
void check(int g) {
  for (int i = 1; i * i <= g; i++)
    if (g % i == 0) {
      fac.push_back(i);
      if (i * i != g) fac.push_back(g / i);
    }
}
int gcd(int a, int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
int main() {
  long long a, b, n, g;
  cin >> a >> b >> n;
  g = gcd(a, b);
  check(g);
  sort(fac.begin(), fac.end());
  while (n--) {
    int l, r;
    cin >> l >> r;
    if (g < l)
      cout << -1 << endl;
    else {
      auto u = lower_bound(fac.begin(), fac.end(), r) - fac.begin();
      auto w = lower_bound(fac.begin(), fac.end(), l) - fac.begin();
      if (u <= fac.size()) {
        if (fac[u] == r)
          cout << fac[u] << "\n";
        else if (u > w)
          cout << fac[u - 1] << endl;
        else
          cout << -1 << endl;
      } else
        cout << -1 << "\n";
    }
  }
  return 0;
}