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:

// Imports
import java.util.*;
import java.io.*;

public class C75 {

    static SortedSet<Long> factors;
    public static void loadPrimeFactorization(long n) {
        factors = new TreeSet<>();
        
        for(long i = 1; i <= Math.sqrt(n); i++) {
            if(n%i == 0) {
                factors.add(i);
                factors.add(n/i);
            }
        }
    }
    
    static long gcd(long a, long b) {
        if(a < 0 || b < 0) {
            return -1;
        }
            
            
        // Everything divides 0 
        while (a != b) {
                
            if(a == 0) {
                return b;
            }
            if(b == 0) {
                return a;
            }
            
            if (a > b) {    
                long floor = a/b;
                a = a - (b*floor);
            }
            else {
                long floor = b/a;
                b = b - (a*floor);     
            }
            
        } 
        return a;
    } 
    
    /**
     * @param args the command line arguments
     * @throws IOException, FileNotFoundException 
     */
    public static void main(String[] args) throws IOException, FileNotFoundException {
        
        // TODO UNCOMMENT WHEN ALGORITHM CORRECT
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        
        
        // TODO code application logic here
        StringTokenizer st = new StringTokenizer(f.readLine());
        long A = Integer.parseInt(st.nextToken());
        long B = Integer.parseInt(st.nextToken());
        long factor = gcd(A, B);
        
        loadPrimeFactorization(factor);
        
        Long[] arr = factors.toArray(new Long[factors.size()]);
        // System.out.println(Arrays.toString(arr));
        
        int N = Integer.parseInt(f.readLine());
        for(int i = 0; i < N; i++) {
            StringTokenizer query = new StringTokenizer(f.readLine());
            long q1 = Integer.parseInt(query.nextToken());
            long q2 = Integer.parseInt(query.nextToken());
            
            int curr = Arrays.binarySearch(arr, q2);
            // System.out.println(curr);
            if(curr >= 0) {
                System.out.println(arr[curr]);
            }
            else {
                if(arr[-1*curr - 2] < q1) {
                    System.out.println(-1);
                }
                else {
                    System.out.println(arr[-1*curr - 2]);
                }
            }
        }
    }

}