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.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class GCD {
    public static void main(String[] args) {
        Scanner sc= new Scanner(System.in);
        int a,b,n;
       a= sc.nextInt();
       b=sc.nextInt();
       n=sc.nextInt();
        ArrayList<Integer> ai= new ArrayList<>();
       int gc=g(a,b);

       for(int i=1;i<=Math.sqrt(gc);i++)
           if(gc%i==0) {
               ai.add(i);
               if(i*i!=gc)
               ai.add(gc/i);
           }
             Collections.sort(ai,Collections.reverseOrder());
       


       while(n-->0) {
           boolean f = false;
           int l = sc.nextInt();
           int h = sc.nextInt();

           if (l > gc)
               System.out.println("-1");

           else if (h == 1)
               System.out.println("1");
           else {
               for (Integer x : ai)
                   if (x >= l && x <= h) {
                       System.out.println(x);
                       f = true;
                       break;
                   }


               if (!f)
                   System.out.println(-1);
           }
       }

    }

    public static int g(int a, int b){
        if(b==0)
            return a;
        return g(b,a%b);
    }
}