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 c75c
{
    private final Scanner sc;
    private static final boolean debug = true;

    static void debug(Object ... objects)
    {
        if(debug)
            System.err.println(Arrays.toString(objects));        
    }

    c75c()
    {
        sc = new Scanner(System.in);
    }

    public static void main(String [] args)
    {
        (new c75c()).solve();
    }
    
    
    void solve()
    {
        long a = sc.nextLong();
        long b = sc.nextLong();
        long m = Math.max(a,b);
        HashSet<Long> fac = new HashSet<Long>();
        for(int i=1;i*i<=m;i++)
        {
            if(a%i == 0 && b%i == 0)
                fac.add((long)i);
            if(a%i == 0&& b%(a/i) == 0 )
                fac.add(a/i);
            if(b%i ==0 && a%(b/i) == 0)
                fac.add(b/i);           

        }

        ArrayList<Long> p = new ArrayList<Long>();
        for(long f:fac)
            p.add(f);
        Collections.sort(p);
        debug(p);
        int n = sc.nextInt();
        for(int i=0;i<n;i++)
        {
            int l = sc.nextInt();
            int h = sc.nextInt();
            int y = p.size()-1;
            while(y>=0 && p.get(y)>h)
                y--;
            if(y>=0 && p.get(y)>=l)
                System.out.println(p.get(y));
            else
                System.out.println(-1);
        }

    }
}