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.io.PrintWriter;
import java.util.StringTokenizer;

public class ProblemC {
    public static void main(String[] args) {
        InputReader in = new InputReader();
        PrintWriter out = new PrintWriter(System.out);

        new ProblemC().solve(in, out);

        out.close();
    }

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

        if (b > a) {
            out.print(-1);

            return;
        }

        if (b == a) {
            out.print(a);

            return;
        }

        int k = (a - b) / (2 * b);
        double p1 = 0;

        if (k == 0) {
            p1 = Double.MAX_VALUE;
        } else {
            p1 = 1.0 * (a - b) / k;
        }

        k = (a + b) / (2 * b);
        double p2 = 1.0 * (a + b) / k;

        out.print(Math.min(p1, p2) / 2);
    }

    static class InputReader {
        public BufferedReader br;
        public StringTokenizer st;

        public InputReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}