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 modifiedGCD {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int a = in.nextInt();
		int b = in.nextInt();
		int n = in.nextInt();
		int gcd = gcd(a, b);
		ArrayList<Integer> al = new ArrayList<Integer>();
		for(int i=1; i<Math.sqrt(gcd)+1; i++) {
			if(gcd%i == 0) {
				al.add(i);
				al.add(gcd/i);
			}
		}

		for(int i=0; i<n; i++) {
			int low = in.nextInt();
			int high = in.nextInt();
			int max = 0;
			int temp = 0;
			for(int j=0; j<al.size(); j++) {
				temp = al.get(j);
				if(temp >= low && temp <= high) {
					if(temp > max)
						max = temp;
				}
			}
			if(max == 0)
				System.out.println(-1);
			else
				System.out.println(max);
		}

		/*for(int i=0; i<n; i++) {
			boolean flag = false;
			int low = in.nextInt();
			int high = in.nextInt();
			if(gcd < low)
				System.out.println(-1);
			else if(gcd <= high)
				System.out.println(gcd);
			else {
				for(int j=high; j>=low; j--) {
					if(gcd%j == 0) {
						flag = true;
						System.out.println(j);
						break;
					}
				}
				if(!flag)
					System.out.println(-1);
			}
		}*/
	}

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

	}
}