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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedOutputStream;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

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

    static class TaskC {
        ArrayList<Integer> divisors;

        public void solve(int testNumber, Kattio in, PrintWriter out) {
            init(in.nextInt(), in.nextInt());

            int q = in.nextInt();
            while (q-- > 0) {
                int left = in.nextInt();
                int right = in.nextInt();

                int ans = -1;
                for (int d : divisors) {
                    if (d >= left && d <= right)
                        ans = d;
                }

                out.println(ans);
            }
        }

        private void init(int a, int b) {
            divisors = new ArrayList<>();
            int n = gcd(a, b);

            for (int i = 1; i * i <= n; ++i) {
                if (n % i == 0) {
                    if (n / i == i)
                        divisors.add(i);
                    else {
                        divisors.add(i);
                        divisors.add(n / i);
                    }
                }
            }

            Collections.sort(divisors);
        }

        int gcd(int a, int b) {
            if (b == 0)
                return a;

            return gcd(b, a % b);
        }

    }

    static class Kattio extends PrintWriter {
        private BufferedReader r;
        private String line;
        private StringTokenizer st;
        private String token;

        public Kattio(InputStream i) {
            super(new BufferedOutputStream(System.out));
            r = new BufferedReader(new InputStreamReader(i));
        }

        public Kattio(InputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        private String peekToken() {
            if (token == null)
                try {
                    while (st == null || !st.hasMoreTokens()) {
                        line = r.readLine();
                        if (line == null) return null;
                        st = new StringTokenizer(line);
                    }
                    token = st.nextToken();
                } catch (IOException e) {
                }
            return token;
        }

        private String nextToken() {
            String ans = peekToken();
            token = null;
            return ans;
        }

    }
}