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 main() {
  int x, y;
  cin >> x >> y;
  int a = min(x, y);
  int b = max(x, y);
  int i;
  vector<int> cd;
  for (i = 1; i * i <= a; i++) {
    if (a % i == 0) {
      if (i * i == a) {
        if (b % i == 0) {
          cd.push_back(i);
        }
      } else {
        if (b % i == 0) {
          cd.push_back(i);
        }
        if ((a % (a / i) == 0) && (b % (a / i) == 0)) {
          cd.push_back(a / i);
        }
      }
    }
  }
  sort(cd.begin(), cd.end());
  int len = cd.size();
  int t;
  cin >> t;
  while (t--) {
    int low, high, ans = -1;
    cin >> low >> high;
    int l = 0, r = len - 1;
    while (l <= r) {
      int mid = l + (r - l) / 2;
      if (cd[mid] > high) {
        r = mid - 1;
      } else if (cd[mid] < low) {
        l = mid + 1;
      } else {
        ans = cd[mid];
        l = mid + 1;
      }
    }
    cout << ans << endl;
  }
}