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.*;

public class Main implements Runnable {
	String file = "template";

	private void solve() throws IOException {
		BigInteger a = new BigInteger(next());
		BigInteger b = new BigInteger(next());
		int gcd = a.gcd(b).intValue();
		ArrayList<Integer> cds = new ArrayList<Integer>();
		for (int i  = 1; i*i <= gcd; ++i) {
			if (gcd % i  == 0) {
				cds.add(i);
				if (i * i != gcd) {
					cds.add(gcd / i);
				}
			}
		}
		Collections.sort(cds);
		int n = nextInt();
		for (int i = 0; i < n; ++i) {
			int low = nextInt(); 
			int high = nextInt();
			int l  = 0; 
			int r = cds.size();
			while (r - l > 1) {
				int m = l + (r - l) / 2;
				if (cds.get(m) > high) {
					r = m;
				} else {
					l = m;
				}
			}
			if (cds.get(l) >= low) {
				out.println(cds.get(l));
			} else {
				out.println(-1);
			}
		}
	}
	
	public static void main(String[] args) {
		new Thread(new Main()).start();
	}

	BufferedReader br;
	StringTokenizer tok;
	PrintWriter out;

	@Override
	public void run() {
		try {
			Locale.setDefault(Locale.US);
			if (Boolean.getBoolean("SpbAU")) {
				br = new BufferedReader(new FileReader(file + ".in"));
				out = new PrintWriter(System.out);
			} else {
				br = new BufferedReader(new InputStreamReader(System.in, "windows-1251"));
				out = new PrintWriter(System.out);
			}
			tok = new StringTokenizer("");
			while (hasNext()) {
				solve();
			}
			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}
	
	boolean hasNext() throws IOException {
		while (!tok.hasMoreElements()) {
			String line = br.readLine();
			if (line == null) {
				return false;
			}
			tok = new StringTokenizer(line);
		}
		return true;
	}
	
	String next() throws IOException {
		if (hasNext()) {
			return tok.nextToken();
		}
		throw new IOException("No more tokens");
	}
	
	int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	
	long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	
	double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
}