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.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.util.Locale;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Tifuera
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        long a = in.nextInt();
        long b = in.nextInt();

        double result = -1d;
        if (a - b >= 2 * b) {
            long k = (a - b) / (2 * b);
            result = (a - b) / (2d * k);
        }

        if (a >= b) {
            long k = (a + b) / (2 * b);
            if (result < 0) {
                result = (a + b) / 2d * k;
            } else {
                result = Math.min(result, (a + b) / (2d * k));
            }
        }

        out.println(String.format(Locale.US, "%.12f", result));
    }


}

class InputReader {
    private BufferedReader reader;
    private String[] currentArray;
    private int curPointer;

    public InputReader(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
    }


    public int nextInt() {
        if ((currentArray == null) || (curPointer >= currentArray.length)) {
            try {
                currentArray = reader.readLine().split(" ");
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            curPointer = 0;
        }
        return Integer.parseInt(currentArray[curPointer++]);
    }

}