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.*;
import java.io.*;

public class C{
	public static NavigableSet<Integer> factor(int n)
	{
		NavigableSet<Integer> ns = new TreeSet();
		for(int i=1;i*i<=n;i++)
		{
			if(n%i==0)
			{
				ns.add(i);
				ns.add(n/i);
			}
		}
		return ns;
	}
	public static void main(String[] args)
	{
		FastScanner fs = new FastScanner();
		int a = fs.nextInt(); int b = fs.nextInt();
		NavigableSet<Integer> ns = new TreeSet();
		ns = factor(a);
		ns.retainAll(factor(b));
		int q = fs.nextInt();
		for(int i=0;i<q;i++)
		{
			int left = fs.nextInt(); int right = fs.nextInt();
			Integer ans = ns.floor(right);
			if(ans != null && ans>=left)
			{
				System.out.println(ans);
			}
			else
			{
				System.out.println(-1);
			}
		}
	}






	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

}