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.*;

public class G {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		ArrayList<Integer> gcd = new ArrayList<>();
		Scanner scanner = new Scanner(System.in);
		int a = scanner.nextInt();
		int b = scanner.nextInt();
		if (a > b) {
			int temp = a;
			a = b;
			b = temp;
		}
		for (int i = 1; i * i <= a; i++) {
			if (a % i == 0) {
				if (b % i == 0)
					gcd.add(i);
				int k = a / i;
				if (k * k == a)
					break;
				if (b % k == 0)
					gcd.add(k);
			}
		}
		Collections.sort(gcd);
		int m = scanner.nextInt();
		while (m > 0) {
			int y = scanner.nextInt();
			int x = scanner.nextInt();
			System.out.println(search(gcd, x, y));
			m--;
		}

	}

	public static int search(ArrayList<Integer> gcd, int x, int y) {
		int L = 0, R = gcd.size() - 1;
		while (L <= R) {
			int mid = (L + R) / 2;
			if (gcd.get(mid) > x) {
				R = mid - 1;
			} else
				L = mid + 1;
		}
		if (gcd.get(R) < y)
			return -1;
		else
			return gcd.get(R);
	}

}