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.PrintWriter;
import java.util.Scanner;
import java.util.TreeSet;

public class C {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int a = in.nextInt();
        int b = in.nextInt();
        TreeSet<Integer> del = new TreeSet<Integer>();
        for (int i = 1; 1L * i * i <= a && 1L * i * i <= b; ++i) {
            if (a % i == 0 && b % i == 0) {
                del.add(i);
            }
            if (a % i == 0 && b % (a / i) == 0) {
                del.add(a / i);
            }
            if (b % i == 0 && a % (b / i) == 0) {
                del.add(b / i);
            }
        }
        int[] dels = new int[del.size()];
        int dn = 0;
        for (int d: del) {
            dels[dn++] = d;
        }
        int n = in.nextInt();
        for (int i = 0; i < n; ++i) {
            int left = in.nextInt();
            int right = in.nextInt();
            int lo = 0;
            int hi = dn - 1;
            while (hi > lo + 1) {
                int mid = (lo + hi) / 2;
                if (dels[mid] <= right) {
                    lo = mid;
                } else {
                    hi = mid;
                }
            }
            if (dels[hi] <= right && dels[hi] >= left) {
                out.println(dels[hi]);
            } else if (dels[lo] <= right && dels[lo] >= left) {
                out.println(dels[lo]);
            } else {
                out.println(-1);
            }
        }
        in.close();
        out.close();
    }   
}