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.awt.Point;
import java.awt.geom.Line2D;
import java.awt.geom.Point2D;
import java.io.*;
import java.math.BigInteger;
import static java.math.BigInteger.*;
import java.util.*;
public class C{
	
	void solve()throws Exception
	{				
		int a=nextInt();
		int b=nextInt();
		HashSet<Integer>x=get(a);
		HashSet<Integer>y=get(b);
		HashSet<Integer>z=new HashSet<Integer>();
		for(int num: x)
			if(y.contains(num))
				z.add(num);
		Integer[]all=z.toArray(new Integer[0]);
		Arrays.sort(all);
		int Q=nextInt();
		for(int q=1;q<=Q;q++)
		{
			int low=nextInt();
			int high=nextInt();
			int res=-1;
			if(high>=all[0])
			{
				int l=0;
				int h=all.length;
				while(h-l>1)
				{
					int m=(l+h)/2;
					if(all[m]<=high)
						l=m;
					else
						h=m;
				}
				if(all[l]>=low)
					res=all[l];
			}
			System.out.println(res);
		}
	}	
	HashSet<Integer> get(int n)
	{
		HashSet<Integer>res=new HashSet<Integer>();
		for(int i=1;i*i<=n;i++)
			if(n%i==0)
			{
				res.add(i);
				res.add(n/i);
			}
		return res;
	}
	BufferedReader reader;
	PrintWriter writer;
	StringTokenizer stk;
	void run()throws Exception
	{
		reader=new BufferedReader(new InputStreamReader(System.in));
		stk=null;
		writer=new PrintWriter(System.out);
		solve();
		reader.close();
		writer.close();
	}
	int nextInt()throws Exception
	{
		return Integer.parseInt(nextToken());
	}
	long nextLong()throws Exception
	{	
		return Long.parseLong(nextToken());
	}
	double nextDouble()throws Exception
	{		
		return Double.parseDouble(nextToken());
	}
	String nextString()throws Exception
	{
		return nextToken();
	}
	String nextLine()throws Exception
	{
		return reader.readLine();
	}
	String nextToken()throws Exception
	{
		if(stk==null || !stk.hasMoreTokens())
		{
			stk=new StringTokenizer(nextLine());
			return nextToken();
		}
		return stk.nextToken();
	}
	
	public static void main(String[]args) throws Exception
	{	
		new C().run();

	}
	
}