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.*;

public class A {
    public static void solution(BufferedReader reader, PrintWriter out)
            throws IOException {
        In in = new In(reader);
        int a = in.nextInt(), b = in.nextInt();
        if (a < b)
            out.println(-1);
        else if (a == b)
            out.println(a);
        else {
            // up
            int k1 = (int) ((a - b) / (2.0 * b));
            double x1 = (a - b) / (2.0 * k1);
            // down
            int k2 = (int) ((a + b) / (2.0 * b));
            double x2 = (a + b) / (2.0 * k2);
            out.println(Math.min(x1, x2));
        }
    }

    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(
                new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(
                new BufferedWriter(new OutputStreamWriter(System.out)));
        solution(reader, out);
        out.close();
    }

    protected static class In {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public In(BufferedReader reader) {
            this.reader = reader;
        }

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

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

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

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