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.math.*;
import java.io.*;
import java.text.DecimalFormat;
import java.math.BigInteger;
public class Main{
    static int d=20,n;
    static int mod=1000000007 ;
    static  ArrayList<ArrayList<Integer>> arr;
    static int[] a,b,c; 
    public static void main(String[] args)  throws IOException {
        s.init(System.in);   
        
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int a,b,c;
        a=s.ni();
        b=s.ni();
        c=gcd(a,b);

        int n=s.ni();
        while(n--!=0){
            int x,y;
            x=s.ni();
            y=s.ni();
            int l=(int)Math.floor(c*1.0/x);
            int h=(int)Math.ceil(c*1.0/y);
            int ans=-1;
            for(int i=h;i<=l;i++){
                if(c%i==0){
                    ans=c/i;
                    break;
                }
            }
            out.println(ans);
        }
        
        out.close();
    }
    public static int gcd(int x,int y){
        if(x%y==0)
            return y;
        else
            return gcd(y,x%y);
    }
  
       
    public static class s {
        static BufferedReader reader;
        static StringTokenizer tokenizer;
 
        /** call this method to initialize reader for InputStream */
        static void init(InputStream input) {
            reader = new BufferedReader(
                        new InputStreamReader(input) );
            tokenizer = new StringTokenizer("");
        }   
 
        /** get next word */
        static String ns() throws IOException {
            while ( ! tokenizer.hasMoreTokens() ) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                    reader.readLine() );
            }
            return tokenizer.nextToken();
        }
 
        static int ni() throws IOException {
            return Integer.parseInt( ns() );
        }
    
        static double nd() throws IOException {
            return Double.parseDouble( ns() );
        }
        static long nl() throws IOException {
            return Long.parseLong( ns() );
        }
        
    }
}