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 i, j, n, a, b;
int num = 0;
vector<int> v;
int main() {
  cin >> a >> b >> n;
  for (i = 1; i * i <= a; i++) {
    if (a % i == 0 && b % i == 0) {
      v.push_back(i);
    }
    if (i * i < a && a % i == 0) {
      int j = a / i;
      if (b % j == 0) {
        v.push_back(j);
      }
    }
  }
  sort(v.begin(), v.end());
  for (i = 0; i < n; i++) {
    int x, y;
    cin >> x >> y;
    int ans = -1;
    for (j = 0; j < v.size(); j++) {
      if (v[j] >= x && v[j] <= y) ans = v[j];
    }
    cout << ans << endl;
  }
  return 0;
}