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;
  else
    return gcd(b, a % b);
}
int main(int argc, char const* argv[]) {
  int a, b;
  cin >> a >> b;
  int divisor = gcd(a, b);
  vector<int> v;
  for (int i = 1; i * i <= divisor; i++) {
    if (divisor % i == 0) {
      v.push_back(i);
      if (i * i != divisor) v.push_back(divisor / i);
    }
  }
  sort(v.begin(), v.end());
  int n;
  cin >> n;
  while (n--) {
    int low, high;
    cin >> low >> high;
    int i;
    for (i = v.size() - 1; i >= 0; i--) {
      if (v[i] >= low && v[i] <= high) {
        break;
      }
    }
    if (i >= 0)
      cout << v[i] << endl;
    else
      cout << -1 << endl;
  }
  return 0;
}