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.lang.*;
import java.math.*;
import java.io.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;

// Modified GCD
// 2012/11/6
public class P075C{
	BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

	int a, b;
	int n;
	int[] lows, highs;

	void run(){
		try{
			String[] ss=br.readLine().split(" ");
			a=Integer.parseInt(ss[0]);
			b=Integer.parseInt(ss[1]);
			n=Integer.parseInt(br.readLine());
			lows=new int[n];
			highs=new int[n];
			for(int i=0; i<n; i++){
				ss=br.readLine().split(" ");
				lows[i]=Integer.parseInt(ss[0]);
				highs[i]=Integer.parseInt(ss[1]);
			}
			solve();
		}catch(IOException e){}
	}

	void solve(){
		TreeSet<Integer> set=new TreeSet<Integer>(divisor(gcd(a, b)));
		StringBuilder sb=new StringBuilder();
		for(int i=0; i<n; i++){
			Integer d=set.floor(highs[i]);
			sb.append((d!=null&&d>=lows[i])?d:-1).append('\n');
		}
		print(sb.toString());
	}

	ArrayList<Integer> divisor(int n){
		ArrayList<Integer> list=new ArrayList<Integer>();
		for(int i=1; i*i<=n; i++){
			if(n%i==0){
				list.add(i);
				if(n/i!=i){
					list.add(n/i);
				}
			}
		}
		return list;
	}

	int gcd(int a, int b){
		return a==0?b:gcd(b%a, a);
	}

	void print(String s){
		System.out.print(s);
	}

	public static void main(String[] args){
		Locale.setDefault(Locale.US);
		new P075C().run();
	}
}