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.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import static java.lang.Math.*;

public class BetaRound67_C implements Runnable {

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

	public static void main(String[] args) {
		new Thread(null, new BetaRound67_C(), "", 256 * (1L << 20)).start();
	}

	public void run() {
		try {
			long t1 = System.currentTimeMillis();
			if (System.getProperty("ONLINE_JUDGE") != null) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			} else {
				in = new BufferedReader(new FileReader("input.txt"));
				out = new PrintWriter("output.txt");
			}
			Locale.setDefault(Locale.US);
			solve();
			in.close();
			out.close();
			long t2 = System.currentTimeMillis();
			System.err.println("Time = " + (t2 - t1));
		} catch (Throwable t) {
			t.printStackTrace(System.err);
			System.exit(-1);
		}
	}

	String readString() throws IOException {
		while (!tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}

	long readLong() throws IOException {
		return Long.parseLong(readString());
	}

	double readDouble() throws IOException {
		return Double.parseDouble(readString());
	}

	// solution
	
	int gcd(int a, int b) {
		if (b == 0) return a;
		return gcd(b, a % b);
	}
	
	TreeSet<Integer> factorization(int x) {
		TreeSet<Integer> set = new TreeSet<Integer>();
		for (int i = 1; i * i <= x; i++) {
			if (x % i == 0) {
				set.add(i);
				set.add(x / i);
			}
		}
		return set;
	}
	
	void solve() throws IOException {
		int a = readInt();
		int b = readInt();
		int g = gcd(a, b);
		TreeSet<Integer> set = factorization(g);
		int n = readInt();
		while (n --> 0) {
			int L = readInt();
			int R = readInt();
			Integer ans = set.floor(R);
			if (ans == null || ans < L) {
				out.println(-1);
			} else {
				out.println(ans);
			}
		}
	}

}