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.util.Arrays;
import java.util.LinkedList;

public class SRM67_3 {
    public static int gcd(int a,int b){
       if(a<b)return gcd(b,a);
       if(b==0)return a;
       return gcd(b,a%b);
    }
    public static void main(String[] args) throws NumberFormatException,
            IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String []s = in.readLine().split(" ");
        int a = Integer.parseInt(s[0]);
        int b = Integer.parseInt(s[1]);
        int gcd = gcd(a,b);
        LinkedList<Integer> divisors = new LinkedList<Integer>();
        
        divisors.add(1);
        for (int i = 2; i*i <= gcd; i++) {
            if(gcd%i==0){
                divisors.add(i);
                divisors.add(gcd/i);
            }
        }
        divisors.add(gcd);
        int div [] = new int [divisors.size()];
        for (int i = 0; i < div.length; i++) {
            div[i] = divisors.get(i);
        }
        Arrays.sort(div);
        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 res = -1;
            for (int y=div.length-1 ; y>=0 ; y--) {
                if(div[y]>=lo && div[y]<=hi){
                res = div[y];
                break;
                }
            }
            System.out.println(res);
        }
        
    }
}