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(long long a, long long b) {
  if (a == 0)
    return b;
  else
    return gcd(b % a, a);
}
set<long long> divs;
vector<long long> vecDivs;
void allDiv(long long a) {
  long long sqA = sqrt(a) + 1;
  for (int i = 1; i < sqA; i++) {
    if (a % i == 0) {
      divs.insert(i);
      divs.insert(a / i);
    }
  }
  set<long long>::iterator it;
  for (it = divs.begin(); it != divs.end(); it++) vecDivs.push_back(*it);
}
long long BS(long long srchLow, long long srchHigh) {
  long long high = vecDivs.size();
  long long low = 0;
  long long mid;
  long long ans = -1;
  while (low <= high) {
    mid = (low + high) / 2;
    if (vecDivs[mid] > srchHigh) {
      high = mid - 1;
    } else if (vecDivs[mid] < srchLow) {
      low = mid + 1;
    } else if (vecDivs[mid] >= srchLow && vecDivs[mid] <= srchHigh) {
      ans = vecDivs[mid];
      low = mid + 1;
    }
  }
  return ans;
}
int main() {
  long long a, b;
  scanf("%lld", &a);
  scanf("%lld", &b);
  allDiv(gcd(a, b));
  int n;
  scanf("%d", &n);
  while (n--) {
    long long low, high;
    scanf("%lld", &low);
    scanf("%lld", &high);
    if (low == high) {
      if (gcd(a, b) % low == 0)
        printf("%lld\n", low);
      else
        printf("-1\n");
    } else
      printf("%lld\n", BS(low, high));
  }
  return 0;
}