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.*;

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);
        Solver solver = new Solver();
        solver.solve(1, in, out);
        out.close();
    }

    public static class Pair<X, Y> {
        public X x;
        public Y y;
        public Pair(X x, Y y) {
            this.x = x;
            this.y = y;
        }
    }

    static class Solver {
        int a, b, n;
        List<Integer> divs;
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            a = in.nextInt();
            b = in.nextInt();
            Set<Integer> diva = new TreeSet<>();
            for (int i = 1; i * i <= a; i++) {
                if (a % i == 0) {
                    diva.add(i);
                    diva.add(a / i);
                }
            }
            divs = new ArrayList<>();
            for (Integer d: diva) {
                if (b % d == 0) {
                    divs.add(d);
                }
            }

            n = in.nextInt();

            for (int i = 0; i < n; i++) {
                int l, r;
                l = in.nextInt();
                r = in.nextInt();
                int ans = binSearch(r);
                if (ans >= l) {
                    System.out.println(ans);
                } else {
                    System.out.println(-1);
                }
            }
        }

        private int binSearch(int x) {
            int l = -1;
            int r = divs.size();
            while (r - l > 1) {
                int mid = (l + r) / 2;
                if (divs.get(mid) <= x) {
                    l = mid;
                } else {
                    r = mid;
                }
            }
            if (l != -1) {
                return divs.get(l);
            }
            return l;
        }
    }

    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());
        }

        public long nextLong() { return Long.parseLong(next()); }
    }
}