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 z3 {
    public static void main(String[] args) throws IOException {
        new z3().run();
    }

    PrintWriter out;
    StringTokenizer in;
    BufferedReader br;
    boolean eof = false;

    String file = "a";

    void run() throws IOException {
        // br = new BufferedReader(new FileReader(file + ".in"));
        br = new BufferedReader(new InputStreamReader(System.in));
        // out = new PrintWriter(file + ".out");
        solve();
        // out.flush();
    }

    String nextToken() throws IOException {
        try {
            while (in == null || !in.hasMoreTokens()) {
                in = new StringTokenizer(br.readLine());
            }
            return in.nextToken();
        } catch (Exception e) {
            eof = true;
            return "";
        }
    }

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

    void solve() throws IOException {
        int a = nextInt(), b = nextInt();
        ArrayList<Integer> divs = new ArrayList<Integer>();
        ArrayList<Integer> divisors = new ArrayList<Integer>();
        int min = Math.min(a, b);
        for (int i = 1; i * i <= min; i++) {
            if (min % i == 0) {
                divs.add(i);
                int other = min / i;
                if (i != other) {
                    divs.add(other);
                }
            }
        }
        for (int p : divs) {
            if (a % p == 0 && b % p == 0) {
                divisors.add(p);
            }
        }
        int n = nextInt();
        for (int i = 0; i < n; i++) {
            int low = nextInt(), high = nextInt();
            int max = -1;
            for (int tmp : divisors) {
                if (tmp >= low && tmp <= high) {
                    max = Math.max(tmp, max);
                }
            }
            System.out.println(max);
        }
    }
}