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 gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
int main() {
  int a, b;
  vector<int> factors;
  scanf("%d%d", &a, &b);
  int g = gcd(a, b);
  for (int i = 1; i * i <= g; i++) {
    if (g % i == 0) {
      if (i * i == g) {
        factors.push_back(i);
      } else {
        factors.push_back(i);
        factors.push_back(g / i);
      }
    }
  }
  sort(factors.begin(), factors.end());
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d%d", &a, &b);
    int x = upper_bound(factors.begin(), factors.end(), b) - factors.begin();
    x--;
    if (factors[x] <= b && factors[x] >= a)
      printf("%d\n", factors[x]);
    else
      puts("-1");
  }
  return 0;
}