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.Arrays;
import java.util.Set;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Nasko
 */
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);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {

            int A = in.nextInt();
            int B = in.nextInt();

            int min = Math.min(A, B);
            int max = Math.max(A, B);
            B = max;
            A = min;

            Set<Integer> hs = new HashSet<Integer>();
            for (int i = 1; i * i <= B; ++i) {
                if ((B % i == 0)) {

                    if (A % i == 0) hs.add(i);
                    int left = B / i;
                    if (B % left == 0 && (A % left == 0)) hs.add(B / i);

                }
            }
            int[] elem = new int[hs.size()];
            int id = 0;
            for (int i : hs) elem[id++] = i;
            Arrays.sort(elem);

            int Q = in.nextInt();

            for (int q = 0; q < Q; ++q) {
                int l = in.nextInt();
                int r = in.nextInt();

                int low = 0;
                int high = elem.length - 1;

                int best = Integer.MIN_VALUE;
                while (low <= high) {
                    int mid = (low + high) >> 1;
                    if (elem[mid] >= l && elem[mid] <= r) {
                        best = Math.max(best, elem[mid]);
                        low = mid + 1;
                    } else if (elem[mid] > r) {
                        high = mid - 1;
                    } else low = mid + 1;
                }
                if (best == Integer.MIN_VALUE)
                    out.println(-1);
                else out.println(best);
            }
        }

    }

    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());
        }

    }
}