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 {

    int gcd(int a, int b) {
        int r = a % b;

        while(r != 0) {
            a = b;
            b = r;
            r = a % b;
        }

        return b;
    }

    int[] makeDiv(int a, int b) {
        TreeSet<Integer> s = new TreeSet<Integer>();
        
        int g = gcd(a, b);
        s.add(g);
        s.add(1);
        for(int i = 2; i * i <= g; ++i)
            if(g % i == 0) {
                s.add(i);
                s.add(g / i);
            }

        int[] ans = new int[s.size()];
        int count = 0;

        while(!s.isEmpty()) {
            ans[count] = s.last();
            s.remove(ans[count]);
            ++count;
        }

        return ans;
    }

    public void solve() throws IOException {
        int a = nextInt(), b = nextInt();
        int n = nextInt();

        int[] div = makeDiv(a, b);

        while(n-- > 0) {
            int l = nextInt(), h = nextInt();
            
            int ans = -1;
            for(int i = 0; ans == -1 && i < div.length; ++i) {
                int d = div[i];
                if(l <= d && d <= h)
                    ans = d;
            }

            output.println(ans);
        }
    }

    public void run() throws IOException {
        input = new BufferedReader(new InputStreamReader(System.in));
        output = new PrintWriter(System.out);
        solve();
        input.close();
        output.close();
    }

    BufferedReader input;
    PrintWriter output;
    StringTokenizer tok;

    String nextToken() throws IOException {
        while(tok == null || !tok.hasMoreTokens())
            tok = new StringTokenizer(input.readLine());

        return tok.nextToken();
    }

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

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

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

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