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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.*;

public class T3 implements Runnable {
    private void solve() throws IOException {
        int a = nextInt(); int b = nextInt();
        int n = nextInt();
        int g = gcd(a,b);
        HashSet<Integer> divs = new HashSet<Integer>();
        divs.add(1);
        int min = Math.min(a,b);
        int max = Math.max(a, b);
        for(int i = 1; i*i <= g && i <= g; ++i)
        {
            if(g%i ==0)
            {
                divs.add(i);
                divs.add(g/i);
            }
        }
        Integer[] d = new Integer[divs.size()];
        divs.toArray(d);
        Arrays.sort(d);

        for(int i = 0 ; i < n; ++i)
        {
            int x = nextInt(), y = nextInt();
            int beg = 0; int end = d.length-1;
            int idx = 0;
            if(x > d[end])
            {
                writer.println(-1);
                continue;
            }

            while (end != beg)
            {
                idx = (beg + end)/2 + 1;
                if(idx >= d.length || d[idx] >= y)
                {
                    if(d[idx] == y)
                    {
                        beg = idx;
                        break;
                    }
                    end = idx-1;
                }
                else beg = idx;
            }
            int res = -1;
            if(d[beg] >= x && d[beg] <= y)
                res = d[beg];

            writer.println(res);
        }
    }


    int gcd(int a, int b)
    {
        while(b != 0)
        {
            int t = b;
            b = a%b;
            a = t;

        }
        return a;
    }

    public static void main(String[] args) {
        new T3().run();
    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    public void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            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();
    }
}