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;
int a, b;
int v[1000021], sv;
int n;
int Gcd(int x, int y) {
  if (x < y) swap(x, y);
  int r = x % y;
  while (r) {
    x = y;
    y = r;
    r = x % y;
  }
  return y;
}
int main() {
  scanf("%d%d", &a, &b);
  int num = Gcd(a, b);
  for (int i = 1; i * i <= num; ++i) {
    if (num % i == 0) {
      v[++sv] = i;
      if (num / i != i) v[++sv] = num / i;
    }
  }
  sort(v + 1, v + sv + 1);
  scanf("%d", &n);
  while (n--) {
    int low, high;
    scanf("%d%d", &low, &high);
    int l = 1, r = sv;
    while (l < r) {
      int mid = l + r + 1 >> 1;
      if (v[mid] <= high)
        l = mid;
      else
        r = mid - 1;
    }
    if (v[l] >= low)
      printf("%d\n", v[l]);
    else
      printf("-1\n");
  }
  return 0;
}