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 final class modified_gcd
{
	static Scanner sc=new Scanner(System.in);
	static PrintWriter out=new PrintWriter(System.out);
	
	static long gcd(long a,long b)
	{
		if(b==0)
			return a;
		else
			return gcd(b,a%b);
	}
	
	public static void main(String args[]) throws Exception
	{
		long a=sc.nextLong();
		long b=sc.nextLong();
		TreeSet<Long> ts=new TreeSet<Long>();
		long n=gcd(a,b);
		long i;
		for(i=1;(i*i)<n;i++)
		{
			if(n%i==0)
			{
				ts.add(i);
				ts.add(n/i);
			}
		}
		if(i*i==n)
		{
			ts.add(i);
		}
		int q=sc.nextInt();
		while(q>0)
		{
			long l=sc.nextLong();
			long r=sc.nextLong();
			TreeSet<Long> sub=new TreeSet<Long>(ts.subSet(l,r+1));
			if(sub.size()>0)
			{
				out.println(sub.last());
			}
			else
			{
				out.println("-1");
			}
			q--;
		}
		out.close();
	}
}