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;
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int main() {
  int a, b;
  cin >> a >> b;
  int g = gcd(a, b);
  vector<int> d;
  for (int i = 1; i * i <= g; i++) {
    if (g % i == 0) {
      d.push_back(i);
      if ((g / i) > i) d.push_back(g / i);
    }
  }
  sort(d.begin(), d.end());
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int low, high;
    cin >> low >> high;
    int ans = -1;
    int it = lower_bound(d.begin(), d.end(), high) - d.begin();
    if (it == d.size()) it--;
    for (it; it >= 0; it--) {
      if (d[it] >= low && d[it] <= high) {
        ans = d[it];
        break;
      }
    }
    cout << ans << "\n";
  }
  return 0;
}