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.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        C75 solver = new C75();
        solver.solve(1, in, out);
        out.close();
    }

    static class C75 {
        TreeSet<Integer> getFact(int n) {
            TreeSet<Integer> ans = new TreeSet<>();
            for (int i = 1; i * i <= n; ++i) {
                if (n % i == 0) {
                    ans.add(i);
                    if (i * i != n) ans.add(n / i);
                }
            }
            return ans;
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int a = in.nextInt();
            int b = in.nextInt();
            TreeSet<Integer> afact = getFact(a);
            TreeSet<Integer> bfact = getFact(b);
            TreeSet<Integer> div = new TreeSet<>();
            for (int i : afact) {
                if (bfact.contains(i)) div.add(i);
            }
//        System.out.println(div);
            int n = in.nextInt();
            for (int i = 0; i < n; ++i) {
                int x = in.nextInt();
                int y = in.nextInt();
                Integer gcd = div.floor(y);
                if (gcd != null && gcd >= x) {
                    out.println(gcd);
                } else {
                    out.println(-1);
                }
            }
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}