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>
std::set<int> s;
int gcd(int a, int b) {
  while (a != 0 && b != 0) {
    a %= b;
    std::swap(a, b);
  }
  return a + b;
}
int main() {
  int a, b;
  std::cin >> a >> b;
  int g = gcd(a, b);
  int lim = (int)(sqrt((double)g) + 1);
  for (int i = 1; i <= lim; ++i) {
    if (g % i == 0) {
      s.insert(i);
      s.insert(g / i);
    }
  }
  int n;
  std::cin >> n;
  while (n--) {
    std::cin >> a >> b;
    std::set<int>::iterator low = s.lower_bound(a);
    std::set<int>::iterator high = s.upper_bound(b);
    if (high != s.begin() && low != s.end()) {
      --high;
      if (*high >= *low) {
        std::cout << *high << "\n";
      } else {
        std::cout << "-1\n";
      }
    } else {
      std::cout << "-1\n";
    }
  }
  return 0;
}