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;
const int maxn = 20005;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
int main() {
  long long a, b;
  vector<int> gc;
  while (cin >> a >> b) {
    int c = gcd(a, b);
    for (int i = 1; i * i <= c; i++) {
      if (c % i == 0) {
        gc.push_back(i);
        gc.push_back(c / i);
      }
    }
    sort(gc.begin(), gc.end());
    int n;
    cin >> n;
    while (n--) {
      int l, h;
      cin >> l >> h;
      int ans = upper_bound(gc.begin(), gc.end(), h) - gc.begin() - 1;
      if (gc[ans] < l)
        cout << -1 << endl;
      else
        cout << gc[ans] << endl;
    }
  }
  return 0;
}