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.*;
import java.util.StringTokenizer;

public class TaskA {
    StringTokenizer st;
    BufferedReader in;
    PrintWriter out;

    public static void main(String[] args) throws IOException {
        TaskA taskA = new TaskA();
        taskA.open();
        taskA.solve();
        taskA.close();
    }

    String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String str = in.readLine();
            if (str == null) return null;
            else st = new StringTokenizer(str);
        }
        return st.nextToken();
    }

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

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

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

    private void close() {
        try {
            out.close();
            in.close();
        } catch (IOException ignore) {
        }
    }


    private void solve() throws IOException {
        long a = nextInt(), b = nextInt();
        if (a==b) {
            out.println(a);
            return;
        }
        if (a < b) {
            out.println(-1);
            return;
        }

        long k1 = (long)Math.floor((a-b)/2.0/b);
        long k2 = (long)Math.floor((a+b)/2.0/b);
        double x1 = (a-b)/(2.0*k1);
        double x2 = (a+b)/(2.0*k2);

        out.println(Math.min(x1,x2));
    }

    private void open() {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedOutputStream(System.out));
    }
}