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.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;



public class Main {
	public static class FastReader {
			BufferedReader br;
			StringTokenizer root;
			
	 
			public FastReader() {
				br = new BufferedReader(new InputStreamReader(System.in));
			}
	 
			String next() {
				while (root == null || !root.hasMoreTokens()) {
					try {
						root = new StringTokenizer(br.readLine());
					} catch (Exception addd) {
						addd.printStackTrace();
					}
				}
				return root.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 (Exception addd) {
					addd.printStackTrace();
				}
				return str;
			}
		}
	 
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static FastReader sc = new FastReader();
 
	static int mod = (int) (998244353),MAX=(int)(1e5+10);
	static List<Integer>[] edges;
	
	public static void main(String[] args) throws IOException{
	  
		int a = sc.nextInt();
		int b = sc.nextInt();
		int gcd = gcd(a,b);
		TreeSet<Integer> set = new TreeSet<>();
		for(int i=1;i*i<=gcd;++i) {
			if(gcd%i == 0) {
				set.add(i);
				set.add(gcd/i);
			}
		}
		int n = sc.nextInt();
		while(n-->0) {
			int l = sc.nextInt();
			int r = sc.nextInt();
			Integer val = set.floor(r);
			if(val == null || val < l) out.println(-1);
			else out.println(val);
		}
		out.close();
		
	}
	
	static int gcd(int a,int b) {
		if(b == 0) return a;
		return gcd(b,a%b);
	}
}