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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;

/**
 *
 * @author fcocl_000
 */
public class ModifiedGCD2 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        ArrayList<Integer> gcdFact = new ArrayList<>();
        
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String[] line = reader.readLine().split(" ");
        int a = Integer.parseInt(line[0]);
        int b = Integer.parseInt(line[1]);
        
        int gcd = gcd(a,b);
        int i = 1;
        while (i*i <= gcd) {  
            if (gcd % i == 0) {
                if (!gcdFact.contains(i)) {
                    gcdFact.add(i);  
                }
                if (!gcdFact.contains(gcd/i)) {
                    gcdFact.add(gcd/i); 
                }
            }
            i += 1;
        }
        Collections.sort(gcdFact);
        /*
        for (Integer gcdFact1 : gcdFact) {
            System.out.println(gcdFact1);
        }
        */
        
        int n = Integer.parseInt(reader.readLine());
        for (int j = 0; j < n; j++) {
            line = reader.readLine().split(" ");
            int inf = Integer.parseInt(line[0]);
            int sup = Integer.parseInt(line[1]);
            
            int k = Collections.binarySearch(gcdFact, sup);
            if (k < 0) {
                k = -(k+2);
            }
            k = gcdFact.get(k);
            if (k < inf) {
                k = -1;
            }
            System.out.println(k);
        }
    }
    public static int gcd (int x, int y) {
        if (x == 0 || y == 0) {
            return x+y;
        }
        else {
            return gcd(y%x,x);
        }
    }
}