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.io.*;
import java.util.*;
import java.math.*;

import static java.lang.Math.*;

public class Main implements Runnable {
	
	int gcd(int a, int b) {
		while (b != 0) {
			a %= b;
			int temp = a;
			a = b;
			b = temp;
		}
		return a;
	}
	
	void solve() throws Exception {
		int a = sc.nextInt(), b = sc.nextInt();
		int d = gcd(a, b);
		TreeSet<Integer> divset = new TreeSet<Integer>();
		for (int i = 1; i * i <= d; i++) {
			if (d % i == 0) {
				divset.add(i);
				divset.add(d / i);
			}
		}
		int[] divarr = new int[divset.size()];
		int pos = 0;
		for (int div : divset) {
			divarr[pos++] = div;
		}
		int n = sc.nextInt();
	outer:
		for (int i = 0; i < n; i++) {
			int low = sc.nextInt(), high = sc.nextInt();
			for (int j = divarr.length - 1; j >= 0; j--) {
				if (divarr[j] >= low && divarr[j] <= high) {
					out.println(divarr[j]);
					continue outer;
				}
			}
			out.println(-1);
		}
	}
	
	BufferedReader in;
	PrintWriter out;
	FastScanner sc;
	
	static Throwable uncaught;
	
	@Override
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			sc = new FastScanner(in);
			solve();
		} catch (Throwable t) {
			Main.uncaught = t;
		} finally {
			out.close();
		}
	}
	
	public static void main(String[] args) throws Throwable {
		Thread t = new Thread(null, new Main(), "", 128 * 1024 * 1024);
		t.start();
		t.join();
		if (uncaught != null) {
			throw uncaught;
		}
	}

}

class FastScanner {
	
	BufferedReader reader;
	StringTokenizer strTok;
	
	public FastScanner(BufferedReader reader) {
		this.reader = reader;
	}
	
	public String nextToken() throws IOException {
		while (strTok == null || !strTok.hasMoreTokens()) {
			strTok = new StringTokenizer(reader.readLine());
		}
		return strTok.nextToken();
	}
	
	public int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}
	
	public long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}
	
	public double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
	
}