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 sun.reflect.generics.tree.Tree;

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

public class Main {


    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder();
        PrintWriter out = new PrintWriter(System.out);
        TreeSet<Integer> treeSet = new TreeSet<>();
        int a = sc.nextInt() , b = sc.nextInt();
        TreeSet<Integer> common = new TreeSet<>();
        for (int i = 1 ; i * i <= Math.min(a , b) ; ++ i) {
            if (a % i == 0 && b % i == 0) {
                common.add(i);
            }
            if (a % (a / i) == 0 && b % (a / i) == 0) common.add(a / i);
            if (a % (b / i) == 0 && b % (b / i) == 0) common.add(b / i);
        }
        if (Math.max(a , b) % Math.min(a , b) == 0) common.add(Math.min(a , b));
        int n = sc.nextInt();
        while (n -- > 0) {
            int lo = sc.nextInt() , hi = sc.nextInt();
            int res = common.lower(hi + 1);
            if (res >= lo) out.print(res + "\n");
            else out.print("-1\n");
        }
        out.close();

    }

























    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

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

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}