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 threadpractice;
//import java.text.DecimalFormat;
import java.util.*;
import java.io.*;
//import java.math.BigInteger;

public class Main {
    
    public static long gcd(long a,long b){
        if(b>a){
            long temp = a;
            a = b;
            b = temp;
        }
        if(a%b==0){
            return b;
        }
        else{
            return gcd(b,a%b);
        }
    }
    public static ArrayList<Long> geList(long a){
        ArrayList<Long> res = new ArrayList (); 
        int b = (int)Math.sqrt(a);
        int ind = 0;
        for(long i = 1;i<=b;i++){
            if(a%i==0){
                res.add(ind,i);
                res.add(ind+1,a/i);ind++;
            }
        }
        return res;
    }
    
    public static long getGcd(long a[],ArrayList<Long> l){
        int start = 0;
        int end = l.size()-1;
        long gcd = -1;
        
        while(start<=end){
            int mid = (start+end)/2;
            long temp = l.get(mid);
            //System.out.println("000000"+temp);
            if(temp<=a[1]&&temp>=a[0]){
                gcd = temp;
                start = mid+1;
            }
            else if(temp>a[1]){
                end = mid-1;
            }
            else{
                
                start = mid+1;
            }
        }
        return gcd;
    }
    
    //public static int count;
    public static void main(String args[]) {
        try {
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        //
        String s[] = br.readLine().split(" ");
        
        long x = Long.parseLong(s[0]);
        long y = Long.parseLong(s[1]);
        long gcd = gcd(x,y);
        int k = Integer.parseInt(br.readLine());
        ArrayList<Long> list = geList(gcd);
        //System.out.println(list);
        while(k>0){
            String t[] = br.readLine().split(" ");
            long a[] = new long[2];
            a[0] = Long.parseLong(t[0]);
            a[1] = Long.parseLong(t[1]);
            System.out.println(getGcd(a,list));
            k--;
        }
        
        
        
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
   }