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 gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
vector<int> tdiv;
vector<int> p;
vector<int> cnt;
void make(int depth, int v) {
  if (depth == p.size()) {
    tdiv.push_back(v);
    return;
  }
  make(depth + 1, v);
  int tpow = 1;
  for (int i = 1; i <= cnt[depth]; i++) {
    tpow *= p[depth];
    make(depth + 1, v * tpow);
  }
}
int main() {
  int a, b;
  scanf("%d%d", &a, &b);
  int d = gcd(a, b);
  for (int i = 2; i <= d; i++) {
    if (d % i == 0) {
      p.push_back(i);
      cnt.push_back(0);
      while (d % i == 0) {
        cnt.back()++;
        d /= i;
      }
    }
  }
  make(0, 1);
  sort(tdiv.begin(), tdiv.end());
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int low, high;
    scanf("%d%d", &low, &high);
    vector<int>::iterator iter = upper_bound(tdiv.begin(), tdiv.end(), high);
    if (iter == tdiv.begin())
      printf("-1\n");
    else {
      iter--;
      if (low <= *iter && *iter <= high)
        printf("%d\n", *iter);
      else
        printf("-1\n");
    }
  }
}