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.*;

public class Main{
	static int a, b, g;
	static ArrayList v;
	static ArrayList divisors;

	public static void main(String[] args) {
		v = new ArrayList();
		divisors = new ArrayList();
		Scanner sc = new Scanner(System.in);
		a = sc.nextInt();
		b = sc.nextInt();
		g = gcd(a, b);
		primeFactor(g);
		genrateDiv(0, 1);
		Collections.sort(divisors);

		//System.out.println(v);	
		//System.out.println(divisors);
		
		int n = sc.nextInt();
		for (int i = 0; i < n; i++) {
			int l = sc.nextInt(), h = sc.nextInt();
			System.out.println(maxGcdInRange(l, h));
		}
	}

	public static void primeFactor(int g){
		if(g % 2==0 )v.add(2);
		while(g % 2 == 0){
			g /= 2;
		}
		for (int i = 3; i * i <= g; i+=2) {
			if(g%i==0){
				v.add(i);
				while(g%i == 0){
					g/=i;
				}
			}
		}
		if(g > 1)v.add(g);
	}

	public static int gcd(int a, int b){
		if(b == 0)return a;
		return gcd(b, a % b);
	}

	public static void genrateDiv(int index, int mul){
		if(index >= v.size()){
			divisors.add(mul);
			return;
		}
		for(int i = 0; ; i++){
			int t =(int)Math.pow((double)(int)v.get(index), (double)i); 
			if(g % t != 0)break;
			mul *= t;
			if(mul <= g)
				genrateDiv(index + 1, mul);
			mul /= t;
		}
	}
	public static int maxGcdInRange(int l, int h){
		int max = -1;
		for(int i = 0; i < divisors.size(); i++){
			if((int)divisors.get(i) >= l && (int)divisors.get(i) <= h){
				max = (int)divisors.get(i);
			}
			else if((int)divisors.get(i) > h)
				break;
		}
		return max;
	}
}