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.PrintWriter;
import java.math.BigInteger;

public class Main {

    static int gcd(int a, int b){
        if(a<b){
            int buf=a;
            a=b;
            b=buf;
        }
        if(a%b==0) return b;
        else return gcd(a%b, b);
    }
    public static void main(String args[]){
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer s= new StringTokenizer(in.nextLine());
        int a=Integer.parseInt(s.nextToken()),
                b=Integer.parseInt(s.nextToken());
        int div[]=new int[10000];
        int w=0;
        int g=gcd(a,b);
        for(int i=1; i<=Math.sqrt(g); i++){
            if(g%i!=0) continue;
            div[w++]=i;
        }
        int ww=w;
        for(int i=0; i<w; i++)
            div[ww++]=g/div[i];
        int n = Integer.parseInt(in.nextLine());
        for(int i=0; i<n; i++){
            s=new StringTokenizer(in.nextLine());
            int x=Integer.parseInt(s.nextToken()),
                    y=Integer.parseInt(s.nextToken());
            int max=-1;
            for(int j=0; j<ww; j++){
                if(max<div[j]&&div[j]>=x&&div[j]<=y)
                    max=div[j];
            }
            out.println(max);
        }
        out.close();
    }
}