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.ArrayList;
import java.util.TreeSet;

public class ModifiedGCD {
    static BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter printWriter = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    public static void main(String[] args) throws IOException{
        String[] inputString = bufferedReader.readLine().split(" ");
        int a = Integer.parseInt(inputString[0]);
        int b = Integer.parseInt(inputString[1]);
//        int a = 9;
//        int b = 27;
        int greatest = gcd(a,b);
//String[] inputString = null;
        TreeSet<Integer> div = new TreeSet<Integer>();
        generate(div,greatest);

        int n = Integer.parseInt(bufferedReader.readLine());
        for(int i = 0; i < n; i++) {
            inputString = bufferedReader.readLine().split(" ");
            int low = Integer.parseInt(inputString[0]);
            int high = Integer.parseInt(inputString[1]);

           int ans = div.floor(high);
            if(ans == -1 || ans < low) {
                printWriter.println(-1);

            }else printWriter.println(ans);


        }
        printWriter.flush();
        printWriter.close();

    }


    public static int search(ArrayList<Integer> array, int low, int high) {
        int start = 0;
        int end = array.size()-1;
        if(array.get(start) > high) return -1;
        if(array.get(end) < low) return -1;

        int mid = (start + end) >> 1;
        int ans = -1;
        while (start <= end) {
            mid = (start + end) >> 1;
            int ele = array.get(mid);
            if(ele <= high) {
                start = mid + 1;
            } else if(ele > high) {
                end = mid - 1;
            }
        }
        if(start - 1 >= 0 && array.get(start-1) >= low && array.get(start-1) <= high)
            return array.get(start-1);

        return -1;

    }

    public static void generate(TreeSet<Integer> array, int greatest) {
        for (int i = 1; i*i <= greatest; i++) {
            if(greatest % i == 0) {
                array.add(i);
                array.add(greatest / i);
            }
        }
    }

    public static int gcd(int a, int b) {
        while (b != 0) {
        int tmp = b;
            b = a % b;
            a = tmp;
        }
        return a;
    }
}