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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class P075C {

    public static void main(String[] args) {
        Scanner inScanner = new Scanner(System.in);
        int a = inScanner.nextInt();
        int b = inScanner.nextInt();
        while (b != 0) {
            int temp = a;
            a = b;
            b = temp % b;
        }
        int gcd = a;
        List<Integer> divisors = new ArrayList<Integer>();
        for (int i = 1; i * i <= gcd; i++) {
            if (gcd % i == 0) {
                divisors.add(i);
                if (i * i != gcd)
                    divisors.add(gcd / i);
            }
        }
        Collections.sort(divisors);
        int n = inScanner.nextInt();
        main: for (int i = 0; i < n; i++) {
            int low = inScanner.nextInt();
            int high = inScanner.nextInt();
            for (int j = divisors.size() - 1; j >= 0; j--) {
                if (divisors.get(j) >= low && divisors.get(j) <= high) {
                    System.out.println(divisors.get(j));
                    continue main;
                }
            }
            System.out.println(-1);
        }
    }
}