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.Collections;
import java.util.Vector;


public class ModifiedGCD {
	public static void main(String[] args) throws IOException{
		BufferedReader lector = new BufferedReader(new InputStreamReader(System.in)); //lectura de la entrada
		String linea = lector.readLine(); //string de la entrada
		String[] numeros = linea.split(" ");
		
		//Obtenemos numeros
		long a = Integer.parseInt(numeros[0]);
		long b = Integer.parseInt(numeros[1]);
		
		//Nos interesa divisores del gcd
		long gcd = gcd(a,b);
		long raiz = (long) Math.floor(Math.sqrt(gcd))+1;
		//Buscamos divisores del gcd
		Vector<Long> divisores = new Vector<Long>();
		for(long k=1; k<=raiz; k++){
			if(gcd%k == 0){
				divisores.add(k);
				if(k*k != gcd){
					divisores.add(gcd/k);
				}
			}
		}
		
		//Ordenamos los divisores
		Collections.sort(divisores);
		
		//Cantidad de lineas
		int tests = Integer.parseInt(lector.readLine());
		while(tests>0){
			tests--;
			
			//Obtener cotas
			linea = lector.readLine();
			String[] cotas = linea.split(" ");
			long low = Long.parseLong(cotas[0]);
			long high = Long.parseLong(cotas[1]);
			
			int posicion = gcdMod(divisores, high, low);
			if(posicion == -1){
				System.out.println(posicion);
			}else{
				System.out.println(divisores.get(posicion));
			}
		}
		
	}
	
	
	public static long gcd(long a, long b){
		long r = 0;
		long x, y;
		
		if(a>b){
			x = a;
			y = b;
		}else{
			x = b;
			y = a;
		}
		
		r = y;
		
		while(x%y != 0){
			r = x%y;
			x = y;
			y = r;
		}
		return r;
	}
	
	//Busqueda binaria sobre divisores
	public static int gcdMod(Vector<Long> divisores, long high, long low){
		int min = 0;
		int max = divisores.size()-1;
		int guess;
		
		if(divisores.get(max)<= high && divisores.get(max)>= low){
			return max;
		}else{
			while(min <= max){
				guess = (max+min)/2;
				if((divisores.get(guess) <= high && divisores.get(guess)>=low) && divisores.get(guess +1)>high){
					return guess;
				}else if(divisores.get(guess)<high){
					min = guess + 1;
				}else{
					max = guess - 1;
				}
			}
			return -1;
		}
	}

}