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 static java.lang.Math.*;
import static java.lang.System.currentTimeMillis;
import static java.lang.System.exit;
import static java.lang.System.arraycopy;
import static java.util.Arrays.sort;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.fill;
import java.util.*;
import java.io.*;

public class Main {

	public static void main(String[] args) throws IOException {
		try {
			if (new File("input.txt").exists())
				System.setIn(new FileInputStream("input.txt"));
		} catch (SecurityException e) {
		}
		new Thread(null, new Runnable() {
			public void run() {
				try {
					new Main().run();
				} catch (Throwable e) {
					e.printStackTrace();
					exit(999);
				}
			}
		}, "1", 1 << 23).start();
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

	private void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);

		int a = nextInt();
		int b = nextInt();
		int d = gcd(a, b);
		
		int cnt = 0;
		int[] mas = new int[10000];
		for (int i = 1; i * i <= d; i++) 
			if (d % i == 0) {
				mas[cnt++] = i;
				mas[cnt++] = d / i;
			}
		
		sort(mas, 0, cnt);
		int n = nextInt();
		for (int i = 0; i < n; i++) {
			int l = nextInt();
			int r = nextInt();
			int res = -1;
			for (int j = cnt - 1; j >= 0; j--) {
				if (mas[j] < l)
					break;
				if (mas[j] >= l && mas[j] <= r) {
					res = mas[j];
					break;
				}
			}
			System.out.println(res);
		}
		
		in.close();
		out.close();
	}

	int gcd(int a, int b) {
		
		while (b != 0) {
			int tmp = a % b;
			a = b;
			b = tmp;
		}
		
		return a;
	}

	void chk(boolean b) {
		if (b)
			return;
		System.out.println(new Error().getStackTrace()[1]);
		exit(999);
	}
	void deb(String fmt, Object... args) {
		System.out.printf(Locale.US, fmt + "%n", args);
	}
	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}
	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}
	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}
	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}
	boolean EOF() throws IOException {
		while (!st.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null)
				return true;
			st = new StringTokenizer(s);
		}
		return false;
	}
}