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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;

public class Main {
	
	public static void main(String[] args) throws IOException {
		FastReader in = new FastReader();
		
		
		int a =in.nextInt(),b=in.nextInt();
		int gcd=gcd(Math.max(a,b),Math.min(a, b));
		ArrayList<Integer>f=getFactor(gcd);
		Collections.sort(f);
		int n =in.nextInt();
		
		for(int i=0;i<n;i++)
		{
			int lower=in.nextInt(),upper=in.nextInt(),best=-1;
			int l=0,r=f.size()-1;
			while(l<=r)
			{
				int mid=(l+r)/2;
				
				if(f.get(mid)<upper)
				{
					if(f.get(mid)<lower)
						l++;
						else {
							best=f.get(mid);
							l++;
						}
					
				}else if(f.get(mid)>upper)
					r=mid-1;
				else 
				{
					best=f.get(mid);
					break;
				}
				
				
				
				
				
				
			}
			
			
			
			
			
			System.out.println(best);
			
			
			
			
			
		}
		
		
		
		
		
		
		
		
		
		
		
		
		
		
	
	
	
	
	
	
	}

	public static ArrayList<Integer> getFactor(int gcd) {
		ArrayList<Integer>f=new ArrayList<>();
		
		for(int i=1;i*i<=gcd;i++)
		{
			if(gcd%i==0) {
			if(i*i==gcd)
				f.add(i);
			else {
				f.add(i);
				f.add(gcd/i);
			}
			
			
			
			
		}
		}
	
	
	
	
		return f; 
	
	}

	public static int gcd(int a, int b) {

		if(b==0)
			return a; 
		
		return gcd(b,a%b);
	
	
	
	
	}

}

	


class FastReader {
	BufferedReader br;
	StringTokenizer st;

	public FastReader() {
		br = new BufferedReader(new InputStreamReader(System.in));

	}

	String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());

			} catch (IOException e) {
				e.printStackTrace();
			}

		}

		return st.nextToken();

	}

	int nextInt() {

		return Integer.parseInt(next());
	}

	double nextDouble() {

		return Double.parseDouble(next());
	}

	long nextLong() {

		return Long.parseLong(next());
	}

	String nextLine() {
		String str = "";
		try {
			str = br.readLine();

		} catch (IOException e) {

			e.printStackTrace();
		}
		return str;

	}

}