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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.LinkedList;

public class C {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String[] S = in.readLine().split(" ");
        int gcd = Integer.parseInt(""
                + ((new BigInteger(S[0])).gcd(new BigInteger(S[1]))));
        LinkedList<Integer> Div = new LinkedList<Integer>();
        for (int i = 1; i * i <= gcd; i++)
            if (gcd % i == 0) {
                Div.add(i);
                Div.add(gcd / i);
            }
        int n = Integer.parseInt(in.readLine());
        for (int i = 0; i < n; i++) {
            S = in.readLine().split(" ");
            int lo = Integer.parseInt(S[0]);
            int hi = Integer.parseInt(S[1]);
            int max = -1;
            for (int x : Div)
                if (x >= lo && x <= hi)
                    max = Math.max(max, x);
            System.out.println(max);
        }
    }
}