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.util.NavigableSet;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.InputMismatchException;
import java.util.Set;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.TreeSet;
import java.io.Reader;
import java.io.Writer;
import java.util.Collection;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Niyaz Nigmatullin
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		FastPrinter out = new FastPrinter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {

    static NavigableSet<Integer> getDivisors(int n) {
        NavigableSet<Integer> ret = new TreeSet<Integer>();
        for (int i = 1; i * i <= n; i++) {
            if (n % i != 0) {
                continue;
            }
            ret.add(i);
            ret.add(n / i);
        }
        return ret;
    }

	public void solve(int testNumber, FastScanner in, FastPrinter out) {
        int a = in.nextInt();
        int b = in.nextInt();
        NavigableSet<Integer> set = getDivisors(a);
        set.retainAll(getDivisors(b));
        int n = in.nextInt();
        for (int i = 0; i < n; i++) {
            int left = in.nextInt();
            int right = in.nextInt();
            Integer z = set.floor(right);
            if (z != null && z >= left) {
                out.println(z);
            } else {
                out.println(-1);
            }
        }
	}
}

class FastScanner extends BufferedReader {

    boolean isEOF;

    public FastScanner(InputStream is) {
        super(new InputStreamReader(is));
    }

    public int read() {
        try {
            int ret = super.read();
            if (isEOF && ret < 0) {
                throw new InputMismatchException();
            }
            isEOF = ret == -1;
            return ret;
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

    static boolean isWhiteSpace(int c) {
        return c >= -1 && c <= 32;
    }

    public int nextInt() {
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int ret = 0;
        while (!isWhiteSpace(c)) {
            if (c < '0' || c > '9') {
                throw new NumberFormatException("digit expected " + (char) c
                        + " found");
            }
            ret = ret * 10 + c - '0';
            c = read();
        }
        return ret * sgn;
    }

    }

class FastPrinter extends PrintWriter {

    public FastPrinter(OutputStream out) {
        super(out);
    }

    public FastPrinter(Writer out) {
        super(out);
    }


}