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.Iterator;
import java.util.LinkedList;
import java.util.Scanner;

public class ModifiedGcd {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int a = in.nextInt();
        int b = in.nextInt();

        int gcd = gcd(a, b);
        LinkedList<Integer> gcdDiv = generateDivsorsOrdered(gcd);

        int cases = in.nextInt();

        for (int caseIndex = 0; caseIndex < cases; caseIndex++) {
            int lower = in.nextInt();
            int upper = in.nextInt();

            Iterator<Integer> lit = gcdDiv.descendingIterator();

            while (lit.hasNext()) {
                int currentGcd = lit.next();
                if (currentGcd < lower) {
                    System.out.println("-1");
                    break;
                } else if (lower <= currentGcd && currentGcd <= upper) {
                    System.out.println(currentGcd);
                    break;
                }
            }

        }
    }

    static int gcd(int a, int b) {
        while (b != 0) {
            int t = a;
            a = b;
            b = t % b;
        }
        return a; //retrun Math.abs(a); if there are negatives
    }

    //example generateDivsorsOrdered(36) = [1, 2, 3, 4, 6, 9, 12, 18, 36]
    static LinkedList<Integer> generateDivsorsOrdered(int n) {
        LinkedList<Integer> divisors = new LinkedList<>();

        int addIndex = 1;

        divisors.add(1);
        divisors.add(n);

        int i = 2;
        for (; i * i < n; i++) { //note i * i
            if (n % i == 0) {
                divisors.add(addIndex, i);
                addIndex++;
                divisors.add(addIndex, n / i);
            }
        }

        // out of the loop
        if (i * i == n) {
            divisors.add(addIndex, i);
        }

        return divisors;
    }

}