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.PrintWriter;
import java.util.*;
//import java.util.TreeSet;

/**
 * Created by Timur on 14.12.2016.
 */
public class _75C {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int a = in.nextInt();
        int b = in.nextInt();
        int gcd = gcd(a, b);

        ArrayList<Integer> set = new ArrayList<>();

        for(int i = 1; i * i <= gcd; i++){
            if(gcd % i == 0){
                set.add(i);
                if(gcd / i != i)
                    set.add(gcd / i);
            }
        }
        Collections.sort(set);

        int n = in.nextInt();
        for(int i = 0; i < n; i++){
            int low = in.nextInt();
            int high = in.nextInt();
            int index = Collections.binarySearch(set, high);
            if(index >= 0)
                out.println(high);
            else if(index == -1 || set.get(-index - 2) < low)
                out.println(-1);
            else
                out.println(set.get(-index - 2));
        }
        out.close();
    }

    public static int gcd(int a, int b){
        if(b == 0) return a;
        return gcd(b, a % b);
    }
}