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;
map<int, int> mp;
vector<int> v;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int a, b, q;
  cin >> a >> b;
  for (int i = 1; i * i <= a; i++) {
    if (a % i == 0) {
      mp[i]++;
      if ((a / i) != i) mp[a / i]++;
    }
  }
  for (int i = 1; i * i <= b; i++) {
    if (b % i == 0) {
      mp[i]++;
      if ((b / i) != i) mp[b / i]++;
    }
  }
  for (auto &i : mp) {
    if (i.second == 2) v.push_back(i.first);
  }
  cin >> q;
  int l, r, pos;
  while (q--) {
    cin >> l >> r;
    pos = (upper_bound(v.begin(), v.end(), r) - v.begin());
    if (pos == 0)
      cout << -1;
    else if (v[pos - 1] < l)
      cout << -1;
    else
      cout << v[pos - 1];
    cout << "\n";
  }
  return 0;
}