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 Q75C implements Runnable {
    private void solve() throws IOException {
        int a = nextInt();
        int b = nextInt();
        SortedSet<Integer> set = new TreeSet<Integer>();
        int g = gcd(a, b);
        for (int i = 1; i * i <= g; i++) {
            if (g % i == 0) {
                set.add(i);
                set.add(g/i);
            }
        }

        Integer[] dev = set.toArray(new Integer[0]);
        int n = nextInt();
        for (int i = 0; i < n; i++) {
            int low = nextInt();
            int high = nextInt();
            int p = Arrays.binarySearch(dev, high);
            if (p < 0) p = -p - 2;
            if(p<0)p++;
            int dd = dev[p];
            if(dd<=high && dd>=low){
                writer.println(dd);
            }else{
                writer.println(-1);
            }
        }
    }


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

    public static void main(String[] args) {
        new Q75C().run();
    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    public void run() {
        try {

            boolean oj = System.getProperty("ONLINE_JUDGE") != null;

            reader = oj ? new BufferedReader(new InputStreamReader(System.in)) :
                    new BufferedReader(new FileReader(new File("input.txt")));


            tokenizer = null;
            writer = new PrintWriter(System.out);
            long start = System.currentTimeMillis();
            solve();
            reader.close();
            if (!oj) {
                writer.print("\nTime:" + (System.currentTimeMillis() - start));
            }
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

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

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

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

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}