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;
long long GCD(int a, int b) {
  if (b == 0) return a;
  return GCD(b, a % b);
}
vector<long long> getDevisors(int x) {
  vector<long long> ans;
  for (int i = 1; i * i <= x; i++) {
    if (x % i == 0) {
      ans.push_back(i);
      if (x / i != i) ans.push_back(x / i);
    }
  }
  return ans;
}
int main() {
  int a, b;
  scanf("%d%d", &a, &b);
  long long G = GCD(a, b);
  vector<long long> div = getDevisors(G);
  sort(div.begin(), div.end());
  int n;
  scanf("%d", &n);
  while (n--) {
    int F, L;
    scanf("%d%d", &F, &L);
    long long low = lower_bound(div.begin(), div.end(), F) - div.begin();
    long long high = lower_bound(div.begin(), div.end(), L) - div.begin();
    if (low >= div.size()) {
      cout << "-1\n";
      continue;
    }
    if (high >= div.size()) {
      high--;
    } else if (div[high] > L)
      high--;
    if (div[high] >= F && div[high] <= L)
      cout << div[high] << endl;
    else
      cout << "-1\n";
  }
}