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 First {
    private static final Scanner sc = new Scanner(System.in);
    private static final PrintWriter pw = new PrintWriter(System.out);
    private static StringBuffer ans = new StringBuffer();

    public static void main(String[] args) throws Exception {
        int a = sc.nextInt(), b = sc.nextInt();
        ArrayList<Integer> fact = new ArrayList<>();
        int n = gcd(a, b);
        for (int i = 1; i * i <= n; i++) {
            if (n % i == 0 && a % i == 0 && b % i == 0) {
                fact.add(i);
                if (n / i != i && a % (n / i) == 0 && b % (n / i) == 0) fact.add(n / i);
            }
        }
        int[] arr = new int[fact.size()];
        for (int i = 0; i < fact.size(); i++) arr[i] = fact.get(i);
        Arrays.parallelSort(arr);
        int q = sc.nextInt();
        for (int z = 0; z < q; z++) {
            int l = sc.nextInt(), r = sc.nextInt(), low = 0, high = arr.length - 1;
            while (low < high) {
                int mid = low + (high - low) / 2;
                if (arr[mid] > r) high = mid;
                else low = mid + 1;
            }
            for (int j = low; j >= 0; j--) {
                if (arr[j] >= l && arr[j] <= r) {
                    ans.append(arr[j] + "\n");
                    break;
                } else if (arr[j] < l) {
                    ans.append("-1\n");
                    break;
                }
            }
        }
        pw.print(ans);
        sc.close();
        pw.close();
    }

    private static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

}

class Scanner {
    private final BufferedReader br;
    private StringTokenizer st;

    public Scanner(InputStream in) {
        br = new BufferedReader(new InputStreamReader(in));
        st = new StringTokenizer("");
    }

    public String next() throws IOException {
        if (!st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public String nextLine() throws IOException {
        return br.readLine();
    }

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

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

    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public void close() throws IOException {
        br.close();
    }
}

class PrintWriter {
    private final BufferedOutputStream pw;

    public PrintWriter(OutputStream out) {
        pw = new BufferedOutputStream(out);
    }

    public void print(Object o) throws IOException {
        pw.write(o.toString().trim().getBytes());
        pw.flush();
    }

    public void println(Object o) throws IOException {
        print(o + "\n");
    }

    public void close() throws IOException {
        pw.close();
    }
}