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;
vector<int> viktor;
void init(int a, int b) {
  for (int i = 1; i * i <= a; i++) {
    if (a % i == 0) {
      int pom = a / i;
      if (b % i == 0) viktor.push_back(i);
      if (b % pom == 0) viktor.push_back(pom);
    }
  }
  for (int i = 1; i * i <= b; i++) {
    if (b % i == 0) {
      int pomcina = b / i;
      if (a % i == 0) viktor.push_back(i);
      if (a % pomcina == 0) viktor.push_back(pomcina);
    }
  }
  sort(viktor.begin(), viktor.end());
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int a, b;
  cin >> a >> b;
  int q;
  cin >> q;
  int l, r;
  init(a, b);
  vector<int>::iterator it, ptr;
  while (q--) {
    cin >> l >> r;
    it = lower_bound(viktor.begin(), viktor.end(), l);
    ptr = upper_bound(viktor.begin(), viktor.end(), r);
    ptr--;
    if (ptr < it)
      cout << -1 << endl;
    else
      cout << *ptr << endl;
  }
  return 0;
}