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;
inline int read() {
  register int x = 0, f = 0, ch = getchar();
  while ('0' > ch || ch > '9') f ^= ch == '-', ch = getchar();
  while ('0' <= ch && ch <= '9')
    x = (x << 1) + (x << 3) + (ch ^ '0'), ch = getchar();
  return f ? -x : x;
}
vector<int> v;
int ans, T, a, b, l, r, mid;
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
signed main() {
  a = read(), b = read();
  a = gcd(a, b);
  for (register int i = 1; i * i <= a; ++i) {
    if (a % i == 0) {
      v.push_back(i);
      v.push_back(a / i);
    }
  }
  sort(v.begin(), v.end());
  T = read();
  while (T--) {
    l = read(), r = read();
    ans = upper_bound(v.begin(), v.end(), r) - v.begin() - 1;
    printf("%d\n", v[ans] < l ? -1 : v[ans]);
  }
  return 0;
}