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>
int a, b, yue[100000], l[10100], h[10100], p[10100], ans[10100], gs, c, n;
void qsort(int x, int y) {
  int i, j, t, mid;
  i = x;
  j = y;
  mid = yue[(i + j) / 2];
  do {
    while (yue[i] < mid) i++;
    while (yue[j] > mid) j--;
    if (i <= j) {
      t = yue[i];
      yue[i] = yue[j];
      yue[j] = t;
      i++;
      j--;
    }
  } while (i <= j);
  if (i < y) qsort(i, y);
  if (x < j) qsort(x, j);
}
void qsort1(int x, int y) {
  int i, j, t, mid;
  i = x;
  j = y;
  mid = h[(i + j) / 2];
  do {
    while (h[i] > mid) i++;
    while (h[j] < mid) j--;
    if (i <= j) {
      t = h[i];
      h[i] = h[j];
      h[j] = t;
      t = l[i];
      l[i] = l[j];
      l[j] = t;
      t = p[i];
      p[i] = p[j];
      p[j] = t;
      i++;
      j--;
    }
  } while (i <= j);
  if (i < y) qsort1(i, y);
  if (x < j) qsort1(x, j);
}
int gcd(int a, int b) {
  if (a > b) {
    int t;
    t = a;
    a = b;
    b = t;
  }
  if (a == 0)
    return b;
  else
    return gcd(b % a, a);
}
int main() {
  int i, j;
  while (scanf("%d %d", &a, &b) != EOF) {
    c = gcd(a, b);
    for (i = 1; i * i <= c; i++)
      if (c % i == 0) {
        gs++;
        yue[gs] = i;
        gs++;
        yue[gs] = c / i;
      }
    qsort(1, gs);
    scanf("%d", &n);
    for (i = 0; i < n; i++) {
      p[i] = i;
      scanf("%d %d", &l[i], &h[i]);
    }
    qsort1(0, n - 1);
    j = gs;
    for (i = 0; i < n; i++) {
      while (yue[j] > h[i]) j--;
      if (yue[j] < l[i])
        ans[p[i]] = -1;
      else
        ans[p[i]] = yue[j];
    }
    for (i = 0; i < n; i++) printf("%d\n", ans[i]);
  }
  return 0;
}