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 _75C 
{

	public static void main(String[] args) 
	{
		Scanner scan = new Scanner(System.in);
		HashSet<Integer> hs = new HashSet<Integer>();
		int a = scan.nextInt(), b = scan.nextInt(), 
			t = scan.nextInt(), min = Math.max(a, b), i;
		
		hs.add(1);
		if(min < 4)
		{
			min = 4;
		}
		for(i = 2 ; i * i <= min ; i++)
		{
			if(a % i == 0 && b % i == 0)		hs.add(i);
			int div = a / i, div2 = b / i;
			try
			{
				if(a % div == 0 && b % div == 0)	hs.add(div);
				if(a % div2 == 0 && b % div2 == 0)	hs.add(div2);
			}
			catch(Exception E) {}
		}
		if(a == b)	hs.add(a);
		while(t-- > 0)
		{
			int l = scan.nextInt(), r = scan.nextInt(), max = -1;
			for(int x : hs)
			{
				if(x >= l && x <= r)	max = Math.max(max, x);
			}
			System.out.println(max);
		}
	}

}