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 string sep = " ";
unsigned long long gcd(unsigned long long a, unsigned long long b) {
  if (a == 0) {
    return b;
  }
  return gcd(b % a, a);
}
class Compare {
 public:
  bool operator()(unsigned long long a, unsigned long long b) { return a > b; }
};
int main() {
  cin.tie(nullptr);
  cout.tie(nullptr);
  ios_base::sync_with_stdio(false);
  unsigned long long a, b;
  cin >> a >> b;
  int n;
  unsigned long long g = gcd(a, b);
  set<unsigned long long, Compare> gDivisors;
  for (unsigned long long i = 1; i * i <= g; ++i) {
    if (g % i == 0) {
      gDivisors.insert(i);
      gDivisors.insert(g / i);
    }
  }
  cin >> n;
  while (n--) {
    unsigned long long low, high;
    cin >> low >> high;
    bool x = true;
    auto h = gDivisors.lower_bound(high);
    if (h != gDivisors.end() && (*h >= low)) {
      cout << *h << endl;
    } else {
      cout << -1 << endl;
    }
  }
}