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.*;
public class Main3 {
    static long a;
    static long b;
    public static void main(String[]args){
        Scanner sc = new Scanner(System.in);
        a = sc.nextLong();
        b = sc.nextLong();
        int N = sc.nextInt();
        ArrayList<Long>F = new ArrayList<Long>();
        ArrayList<Long> ans = new ArrayList<Long>();
        long n = gcd(a,b);
        for (long j = 1; j<=Math.sqrt(n); j++){
            if (n%j==0){F.add(j);  F.add( n/j );}       
        }
        Collections.sort(F);
        for (int i = 0; i<N; i++){
            long x = sc.nextLong();
            long y = sc.nextLong();
            for (int j = F.size()-1; j>=0; j--){
                long H = F.get(j);
                if (H<=y && H>=x){ans.add(H); break;}
                if (j==0){ans.add(-1L);}
            } 
        }       
        
        for(int i = 0; i<ans.size(); i++){
            System.out.println(ans.get(i));
        }
    }
    public static long gcd(long a, long b) {         
           if (b==0) 
             return a;
           else
             return gcd(b, a % b);
    } 
}
//by Ronex