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.math.*;
import java.util.*;
public class Main {

    public static void main(String[] args) {
    Scanner sc=new Scanner(System.in);
     int t,c,l,u,a=sc.nextInt(),b=sc.nextInt(),T=sc.nextInt();
       
        int gs=gcd(a,b);


        TreeSet<Integer> tree_set = new TreeSet<Integer>();
        for (int i = 1; i * i <= gs; i+=1)
        {
            if (gs % i == 0)
            {
                tree_set.add(i);
                tree_set.add(gs / i);
            }
        }
        ArrayList<Integer> ar=new ArrayList();

        Iterator<Integer> it = tree_set.iterator();
        Integer current = 0;
        while(it.hasNext() ) {
            current = it.next();
          ar.add(current);
        }


        while (T-->0){
        l=sc.nextInt();u=sc.nextInt();c=1;

         if(l>gs){System.out.println(-1);c=11;}
           else for(t=ar.size()-1;t>=0;t--)
                 if(l<=ar.get(t)&&ar.get(t)<=u){System.out.println(ar.get(t));c=11;break;}

           if(c==1)System.out.println(-1);
     }

    
    }

    private static int gcd(int a, int b) {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
        BigInteger gcd = b1.gcd(b2);
        return gcd.intValue();
    }



}