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

public class Solution{
        static int GCD(int a,int b)
        {
                if(a%b==0)
                        return b;
                else
                        return GCD(b,a%b);
        }

        public static void main(String args[]){
                Scanner sc=new Scanner(System.in);
                int m=sc.nextInt();
                int b=sc.nextInt();
                int q=sc.nextInt();

                int value=GCD(m,b);
                ArrayList<Integer> a=new ArrayList<Integer>();
                for(int j=1;j<=Math.sqrt(value);j++)
                {
                        if(value%j==0)
                        {
                                a.add(j);
                                if(j!=(value/j))
                                {
                                        a.add(value/j);
                                }
                        }
                }
                Collections.sort(a);
                while(q-->0)
                {
                         int low=sc.nextInt();
                        int high=sc.nextInt();
                        int l=0;
                        int r=a.size()-1;
                        int mid=0;
                        int cnt=-1;
                        while(l<=r)
                        {
                                mid=(l+r)/2;
                                if(a.get(mid)>=low && a.get(mid)<=high)
                                {
                                        cnt=a.get(mid);
                                        l=mid+1;
                                }
                                else if(a.get(mid)>high)
                                {
                                        r=mid-1;
                                }
                                else
                                        l=mid+1;
                        }
                                System.out.println(cnt);
                }
        }
}