Problem: There is a polyline going through points (0, 0) – (x, x) – (2x, 0) – (3x, x) – (4x, 0) – ... - (2kx, 0) – (2kx + x, x) – .... 

We know that the polyline passes through the point (a, b). Find minimum positive value x such that it is true or determine that there is no such x.

Input

Only one line containing two positive integers a and b (1 ≤ a, b ≤ 109).

Output

Output the only line containing the answer. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9. If there is no such x then output  - 1 as the answer.

Examples

Input

3 1


Output

1.000000000000


Input

1 3


Output

-1


Input

4 1


Output

1.250000000000

Note

You can see following graphs for sample 1 and sample 3. 

<image> <image>

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class C {

    /**
     * @param args
     * @throws IOException 
     */
    public static void main(String[] args) throws IOException
    {
        int a = nextInt();
        int b = nextInt();
        
        if(a < b)
            System.out.println(-1);
        else
            System.out.println((a+b)/(2.0*((a+b)/(2*b))));
        
        
    }

    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer tokenizer = null;

    static long nextLong() throws IOException
    {
        return Long.parseLong(nextToken());
    }

    static double nextDouble() throws IOException
    {
        return Double.parseDouble(nextToken());
    }

    static int nextInt() throws IOException
    {
        return Integer.parseInt(nextToken());
    }

    static String nextToken() throws IOException
    {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
        {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}