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;

/**
 * Created with IntelliJ IDEA.
 * User: nipunas
 * Date: 9/19/15
 * Time: 7:13 PM
 * To change this template use File | Settings | File Templates.
 */
public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String line = br.readLine();
        StringTokenizer st = new StringTokenizer(line);
        double x = Double.parseDouble(st.nextToken()), y =Double.parseDouble(st.nextToken());
        long  k = (int)(Math.floor(x/y)+Math.pow(10,-20));
        if (k%2==0)k-=1.0;
        if (k<=0)
            System.out.println(-1);
        else
        {
            k/=2;
            double  t = (x - y *(2*k+1))/(1.0+2*k+1);
            double ans = y+t;
            System.out.println(ans);
        }
    }
}