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.lang.reflect.Array;
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 CodeChef1 {
    static long min=Integer.MAX_VALUE;
    static long dp[][];
    public static void main(String[] args) throws java.lang.Exception {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    //   int n=Integer.parseInt(br.readLine());
       String str[]=br.readLine().split(" ");
       int a=Integer.parseInt(str[0]);
       int b=Integer.parseInt(str[1]);
       int q=Integer.parseInt(br.readLine());
       int gcd=result(a,b);
       
       ArrayList<Integer> divisors=new ArrayList<>();
       divisors.add(gcd);
       for(int i=1;i*i<=gcd;i++)
       {
           if(gcd%i==0){
           if(gcd/i==i)
           divisors.add(i);
           else
           {
               divisors.add(i);
               divisors.add(gcd/i);
           }
           }
       }
       
       while(q-->0)
       {
           int max=-1;
           String range[]=br.readLine().split(" ");
           int l=Integer.parseInt(range[0]);
           int r=Integer.parseInt(range[1]);
           for(int i=0;i<divisors.size();i++)
           {
               if(divisors.get(i)>=l && divisors.get(i)<=r)
               max=Math.max(max,divisors.get(i));
               
           }
           System.out.println(max);
           
       }
       
    
}
static int result(int a,int b)
{
    if(b==0)
    return a;
    return result(b,a%b);
}
}