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.*;
import java.io.*;

public class Main {
     static long upper_bound(ArrayList<Long> ar,long k)
{
    long s=0;
    long e=ar.size();
    while (s !=e)
    {
        long mid = s+e>>1;
        if (ar.get((int)mid) <=k)
        {
            s=mid+1;
        }
        else
        {
            e=mid;
        }
    }
    
    return s;
}
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        long a=sc.nextInt();
        long b=sc.nextInt();
        TreeMap<Long,Long> hm=new TreeMap<>();
        ArrayList<Long> common=new ArrayList<>();
        for(long i=1;i*i<=a;i++) {
            if(a%i==0) {
                hm.put(i,1l);
                hm.put(a/i,1l);
            }
        }
        for(long i=1;i*i<=b;i++) {
            if(b%i==0) {
                if(hm.containsKey(i))
                common.add(i);
                if(hm.containsKey(b/i))
                common.add(b/i);
            }
        }
        // for(int i=0;i<common.size();i++)
        // System.out.print(common.get((int)i)+" ");
        // System.out.println();
        Collections.sort(common);
        int q=sc.nextInt();
        while(q-->0) {
            long low=sc.nextInt();
            long high=sc.nextInt();
            long ind=upper_bound(common,high);
            ind--;
            if(ind==-1 || common.get((int)ind)<low)
            System.out.println("-1");
            else 
            System.out.println(common.get((int)ind));
        }
    }
}