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.util.*;
import java.io.*;

import static java.lang.Math.*;

public class Main {

    BufferedReader in;
    StringTokenizer st;
    PrintWriter out;

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

    ArrayList<Integer> divisors(int n) {
        ArrayList<Integer> ret = new ArrayList<Integer>();
        for (int i = 1; i * i <= n; ++i) {
            if (n % i == 0) {
                ret.add(i);
                if (i != n / i)
                    ret.add(n / i);
            }
        }
        Collections.sort(ret);
        return ret;
    }

    void solve() throws IOException {
        int a = ni();
        int b = ni();
        int gcd = gcd(a, b);
        List<Integer> divisors = divisors(gcd);
        for (int q = ni(); q > 0; --q) {
            int l = ni();
            int r = ni();
            out.println(gcdInSegm(divisors, gcd, l, r));
        }
    }

    int gcdInSegm(List<Integer> divs, int n, int l, int r) {
        for (int a : divs) {
            int b = n / a;
            if (b >= l && b <= r)
                return b;
        }
        return -1;
    }

    public Main() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

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

    int ni() throws IOException {
        return Integer.valueOf(ns());
    }

    long nl() throws IOException {
        return Long.valueOf(ns());
    }

    double nd() throws IOException {
        return Double.valueOf(ns());
    }

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