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.util.Arrays.*;
import static java.util.Collections.*;
import java.io.*;
import java.math.*;
import java.util.*;

@SuppressWarnings("unused")
public class C {
	public static void main(String[] args) throws Exception {
		int a = nextInt();
		int b = nextInt();
		int gcd = BigInteger.valueOf(a).gcd(BigInteger.valueOf(b)).intValue();
		TreeSet<Integer> divisors = new TreeSet<Integer>();
		for (int i = 1; 1L * i * i <= gcd; i++) {
			if (gcd % i == 0) {
				divisors.add(i);
				divisors.add(gcd / i);
			}
		}
		int n = nextInt();
		for (int i = 0; i < n; i++) {
			int low = nextInt();
			int high = nextInt();
			Integer r = divisors.floor(high);
			if (r != null && low <= r && r <= high)
				System.out.println(r);
			else
				System.out.println(-1);
		}
	}

	static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer("");

	static String next() throws Exception {
		while (!st.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null)
				return null;
			st = new StringTokenizer(s);
		}
		return st.nextToken();
	}

	static int nextInt() throws Exception {
		return Integer.parseInt(next());
	}

	static long nextLong() throws Exception {
		return Long.parseLong(next());
	}

	static double nextDouble() throws Exception {
		return Double.parseDouble(next());
	}
}