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, bool> mymap;
set<int> myset;
int main() {
  ios_base::sync_with_stdio(0);
  int t, i, j;
  int a, b;
  cin >> a >> b;
  for (i = 1; i <= sqrt(a); i++) {
    if (a % i == 0) {
      mymap[i] = true;
      mymap[a / i] = true;
    }
  }
  for (i = 1; i <= sqrt(b); i++) {
    if (b % i == 0) {
      if (mymap.find(i) != mymap.end()) myset.insert(i);
      if (mymap.find(b / i) != mymap.end()) myset.insert(b / i);
    }
  }
  int n;
  cin >> n;
  while (n--) {
    int low, high;
    cin >> low >> high;
    auto it = myset.upper_bound(high);
    if (it == myset.begin()) {
      cout << "-1\n";
      continue;
    }
    --it;
    if (*it >= low)
      cout << *it << "\n";
    else
      cout << "-1\n";
  }
}