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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc=new Scanner(System.in);
		int a,b,n,x,y,s,e,mid,i;
        a=sc.nextInt();
        b=sc.nextInt();
        HashMap<Integer,Integer>map=new HashMap<>();
        for(i=1;i<=Math.sqrt(a);i++){
            if(a%i==0)
            {
                map.put(i,1);
                map.put(a/i,1);
            }
        }
        ArrayList<Integer>ans=new ArrayList<>();
        for(i=1;i<=Math.sqrt(b);i++){
            if(b%i==0){
                if(map.containsKey(i))
                    ans.add(i);
                if(b/i!=i&&map.containsKey(b/i))
                    ans.add(b/i);
            }
        }
        Collections.sort(ans);
        n=sc.nextInt();
        for(i=0;i<n;i++){
            x=sc.nextInt();
            y=sc.nextInt();
            a=-1;
            s=0;
            e=ans.size()-1;
            while(s<=e)
            {
            	 mid=(s+e)/2;
                if(ans.get(mid)>=x&&ans.get(mid)<=y)
                {
                    a=Math.max(ans.get(mid),a);
                    s=mid+1;
                }
                else if(ans.get(mid)<x)
                    s=mid+1;
                else if(ans.get(mid)>y)
                    e=mid-1;
               
            }
            System.out.println(a);
        }
            
	}
}