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.*;

public class File {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        int a = sc.nextInt();
        int b = sc.nextInt();    

        int min = Math.min(a, b);
        int max = Math.max(a, b);

        int queries = sc.nextInt();

        // Precompute all factors of min
        List<Integer> factors = getFactors(min, max);

        for (int q = 0; q < queries; q++) {
            int low = sc.nextInt();
            int high = sc.nextInt();

            // Find largest divisor between low and high.
            int res = search(factors, low, high);

            System.out.println(res);
        }
    }

    public static int search(List<Integer> factors, int low, int high) {
        int lo = 0;
        int hi = factors.size() - 1;
        int largestIndex = -1;

        while (lo <= hi) {
            int mid = lo + (hi - lo) / 2;

            if (factors.get(mid) > high) {
                hi = mid - 1;
            }
            else if (factors.get(mid) < low) {
                lo = mid + 1;
            }
            else {
                largestIndex = Math.max(largestIndex, mid);
                lo = mid + 1;
            }
        }

        return largestIndex == -1 ? -1 : factors.get(largestIndex);
    }

    public static List<Integer> getFactors(int num, int max) {
        List<Integer> list = new ArrayList<>();

        list.add(1);
        if (num == 1) return list;

        if (max % num == 0) {
            list.add(num);
        }

        int root = (int) Math.sqrt(num);

        for (int i = 2; i <= root; i++) {
            if (num % i == 0) {
                if (max % i == 0) list.add(i);

                if (((num / i) != i) && ((max % (num / i)) == 0)) {
                    list.add(num / i);
                }
            }
        }

        Collections.sort(list);
        return list;
    }
}