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.ArrayList;
import java.util.Collections;
import java.util.Scanner;


public class Main {
	static ArrayList<Integer> div = new ArrayList<Integer>();
	public static void main(String[] args){
		Scanner r = new Scanner(System.in);
		
		int a = r.nextInt();
		int b = r.nextInt();
		int gcd = gcd(a, b);
		
		for(int i = 1; i*i <= gcd; i++){
			if(gcd % i == 0){
				div.add(i);
				div.add(gcd/i);
			}
		}

		Collections.sort(div);
		
		int t = r.nextInt();
		while(t-- > 0){
			int bottom = r.nextInt();
			int top = r.nextInt();
			boolean found = false;
			int res = -1;
			
			int hi = div.size()-1;
			int lo = 0;
			
			while(hi >= lo){
				int md = (hi+lo)/2;
//				System.out.printf("(%d, %d)%d\n", lo, hi, md);
				if(bottom <= div.get(md) && div.get(md) <= top){
					res = div.get(md);
					lo = md+1;
				}else if(div.get(md) > top)hi = md-1;
				else if(div.get(md) < bottom)lo = md+1;
			}
//			for(int i = div.size()-1; i >= 0; i--){
//				int divi = div.get(i);
//				if(lo <= divi && divi <= hi){
//					System.out.println(divi);
//					found = true;
//					break;
//				}
//			}
			System.out.println(res);
		}
		
	}
	private static int gcd(int a, int b) {
		if(b == 0)return a;
		return gcd(b, a % b);
	}
	
}