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 gcd_sequence
{
    static FastScanner sc=new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
    static PrintWriter out=new PrintWriter(System.out);
	
	static int gcd(int a,int b)
	{
		if(b==0)
			return a;
		else
			return gcd(b,a%b);
	}
	
	public static void main(String args[]) throws Exception
	{
		int a=sc.nextInt(),b=sc.nextInt();
		int gcd=gcd(a,b);
		List<Integer> list=new ArrayList<Integer>();
		int i;
		for(i=1;(i*i)<gcd;i++)
		{
			if(gcd%i==0)
			{
				list.add(i);
				list.add(gcd/i);
			}
		}
		if(i*i==gcd)
		{
			list.add(i);
		}
		Collections.sort(list);
		int q=sc.nextInt(),n=list.size();
		while(q>0)
		{
			int l=sc.nextInt(),r=sc.nextInt();
			int low=0,high=n-1;
			while(low<high)
			{
				int mid=(low+high+1)>>1;
				if(list.get(mid)<l)
				{
					low=mid+1;
				}
				else if(list.get(mid)>r)
				{
					high=mid-1;
				}
				else
				{
					low=mid;
				}
			}
			if(low>=0 && low<list.size() && list.get(low)>=l && list.get(low)<=r)
			{
				out.println(list.get(low));
			}
			else
			{
				out.println("-1");
			}
			q--;
		}
		out.close();
	}
}
class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }
	
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
	
	public String next() throws Exception {
		return nextToken().toString();
	}
	
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}