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.io.PrintWriter;
import java.util.StringTokenizer;






public class Main{
	static class MyScanner {
	    BufferedReader br;
	    StringTokenizer st;

	    public MyScanner() {
	       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());}

	    long nextLong() {return Long.parseLong(next());}

	    double nextDouble() {return Double.parseDouble(next());}

	    String nextLine(){
	        String str = "";
		  try {
		     str = br.readLine();
		  } catch (IOException e) {
		     e.printStackTrace();
		  }
		  return str;
	    }
	}
		
	
		 public static void main(String[] args) throws IOException {
			 	PrintWriter out = new PrintWriter(System.out);
			    MyScanner sc = new MyScanner();
			 	Main solver = new Main();
				solver.solve(out, sc);
				out.flush();
				out.close();
				
		}
	
		
	
		void solve(PrintWriter out, MyScanner sc) throws IOException{	
	
			int a = sc.nextInt();
			int b = sc.nextInt();
			int n = sc.nextInt();

			outer:
			while(n-- > 0) {
				int l = sc.nextInt();
				int h = sc.nextInt();
				if(l > Math.max(a, b)) out.println(-1);
				else {
					int g = gcd(a, b);
					if(g < l) out.println(-1);
					else if(g >= l && g <= h) out.println(g);
					else if(l == h) {
						if(g % l == 0) out.println(h);
						else out.println(-1);
					}
					else {
						int max = -1;
						for(int i = 1 ; i * i <= g; ++i) {
							if( i > h) break;
							if(g % i == 0) {
								
									if(i >= l && i <= h) max = Math.max(max, i);
									if( g / i >= l && g / i <= h) {
										out.println(g / i);
										continue outer;
									}
								
							}
						}
						out.println(max);
						
					}
				}
			} 
		
			
			
			
			
			
			
 		}
		
		
		int gcd(int a, int b) {
			if(a % b == 0) return b;
			return gcd(b, a % b);
		}
		
		




}