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;
vector<pair<int, int> > factors;
void getFactors(int n) {
  factors.clear();
  int d = 1;
  for (int i = 2; i * i <= n; i += d, d = 2)
    if (n % i == 0) {
      factors.push_back(make_pair(i, 0));
      while (n % i == 0) {
        n /= i;
        factors.back().second++;
      }
    }
  if (n != 1) factors.push_back(make_pair(n, 1));
}
vector<int> divisors;
void getDivisors(int ind = 0, int res = 1) {
  if (ind == (int)factors.size()) {
    divisors.push_back(res);
    return;
  }
  for (int i = 0; i <= factors[ind].second; i++) {
    getDivisors(ind + 1, res);
    res *= factors[ind].first;
  }
}
int main() {
  int a, b, n;
  scanf("%d", &a);
  getFactors(a);
  getDivisors();
  vector<int> d1 = divisors;
  scanf("%d", &b);
  getFactors(b);
  divisors.clear();
  getDivisors();
  vector<int> d2 = divisors;
  sort(d1.begin(), d1.end());
  sort(d2.begin(), d2.end());
  vector<int> cd;
  set_intersection(d1.begin(), d1.end(), d2.begin(), d2.end(),
                   inserter(cd, cd.begin()));
  scanf("%d", &n);
  int low, high, ind;
  for (int i = 0; i < n; i++) {
    scanf("%d%d", &low, &high);
    ind = upper_bound(cd.begin(), cd.end(), high) - cd.begin();
    ind--;
    if (ind == -1 || cd[ind] < low)
      printf("-1\n");
    else
      printf("%d\n", cd[ind]);
  }
  return 0;
}