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.*;
import java.util.*;

public class New {

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

	public static int modifiedGCD(ArrayList<Integer> div, int l, int r) {
		int res = -1;
		for (int i=0; i<div.size(); i++) {
			int temp = div.get(i);
			if (temp >= l && temp <= r) {
				res = Math.max(res, temp);
			}
		}
		return res;
	}

	public static void main(String[] args) throws IOException{
		// File text = new File("input.txt");
		// Scanner sc = new Scanner(text);
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();
		int gcd = GCD(a, b);
		ArrayList<Integer> div = new ArrayList<Integer>();
		for (int i=1; i*i<=gcd; i++) {
			if (gcd%i == 0) {
				div.add(i);
				if (i*i != gcd) {
					div.add(gcd/i);
				}
			}
		}
		int q = sc.nextInt();
		while (q > 0) {
			int l = sc.nextInt();
			int r = sc.nextInt();
			System.out.println(modifiedGCD(div, l, r));
			q -= 1;
		}
	}
}