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 JAVA):

Solution:
import java.util.*;
public class Main {
    static int gcd(int a, int b) {
        return b==0 ? a : gcd(b,a%b);
    }
    static void calc(TreeSet<Integer> set, int G, int i) {
        int tmp = i;
        while(G%i==0) {
            G/=i;
            set.add(tmp);
            tmp*=i;
        }
    }
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int A = in.nextInt();
        int B = in.nextInt();
        int G = gcd(A,B);
        int s = (int)Math.sqrt(G);
        TreeSet<Integer> set = new TreeSet<Integer>();
        set.add(1);
        set.add(G);
        for (int i=2; i<=s; i++) {
            if (G%i==0) {
                calc(set,G,i);
                calc(set,G,G/i);
            }
        }
        int T = in.nextInt();
        for (int t=0; t<T; t++) {
            int low = in.nextInt();
            int high = in.nextInt();
            Integer test = set.lower(high+1);
            if (test != null && test >= low)
                System.out.println(test);
            else
                System.out.println(-1);
        }
    }
}