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 codechef; // 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 Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc=new Scanner(System.in);
		int a=sc.nextInt();
		int b=sc.nextInt();
		ArrayList<Integer> al=new ArrayList<Integer>();
		for(int i=1;i*i<=a;i++){
		    if(i*i==a&&b%i==0){al.add(i);}
		    else if(a%i==0){
		        if(b%i==0)al.add(i);
		        if(b%(a/i)==0)al.add(a/i);
		    }
		}
		Collections.sort(al);
		int t=sc.nextInt();
		for(int l=0;l<t;l++){
		    int lowB=sc.nextInt();
		    int highB=sc.nextInt();
		    int low=0;int high=al.size()-1;
		    int ans=-1;
		    while(low<=high){
		        int mid=low+(high-low)/2;
		        if(al.get(mid)>=lowB&&al.get(mid)<=highB){ans=al.get(mid);low=mid+1;}
		        else if(al.get(mid)<lowB){low=mid+1;}
		        else high=mid-1;
		    }
		    System.out.println(ans);
		}
	}
}