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.Scanner;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class ModifiedGCD {
	public static TreeSet<Integer> divisors;
	public static void main(String[] args){
		Scanner input = new Scanner(System.in);
		StringTokenizer st;
		while (input.hasNextLine()){
			st = new StringTokenizer(input.nextLine());
			int a = Integer.valueOf(st.nextToken());
			int b = Integer.valueOf(st.nextToken());
			st = new StringTokenizer(input.nextLine());
			int n = Integer.valueOf(st.nextToken());
			int c = gcd(a,b);
			getDivs(c);
			for (int i = 0; i < n; i++){
				st = new StringTokenizer(input.nextLine());
				int n1 = Integer.valueOf(st.nextToken());
	            int n2 = Integer.valueOf(st.nextToken());
	            Integer floor = divisors.floor(n2);
	            if (floor == null || floor < n1)
	                System.out.println(-1);
	            else
	                System.out.println(floor);
			}
		}
	}
	
	private static void getDivs(int n){
		divisors = new TreeSet<Integer>();
		int sq = (int)(Math.sqrt(n)) + 1;

        for (int i = 1; i <= sq; i++)
            if (n % i == 0) {
                divisors.add(i);
                divisors.add(n / i);
            }
        divisors.add(n);
	}
	
	private static int gcd(int a, int b) {
        return a == 0 ? b : gcd(b % a, a);
    }
}