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:
//package CodeForces;

import java.util.ArrayList;
import java.util.Scanner;

public class ModifiedGcd {
	
	static int gcd(int a,int b)
	{
		if(b==0)
		{
			return a;
		}
		if(b>a)
		{
			return gcd(b,a);
		}
		return gcd(b,a%b);
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		int a=s.nextInt();
		int b=s.nextInt();
		int gcd=gcd(a,b);
		ArrayList<Integer> arr=new ArrayList<Integer>();
		for(int i=1;i*i<=gcd;i++)
		{
			if(gcd%i==0)
			{
				arr.add(i);
				if(i*i!=gcd)
				{
					arr.add(gcd/i);
				}
			}
		}
		
		int q=s.nextInt();
		while(q>0)
		{
			int l=s.nextInt();int h=s.nextInt();
			int ans=-1;
			for(int i=0;i<arr.size();i++)
			{
				if(arr.get(i)>ans&&arr.get(i)>=l&&arr.get(i)<=h)
				{
					ans=arr.get(i);
				}
			}
			
			System.out.println(ans);
			q--;
		}

	}

}