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

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

    static class TaskA {
        public void solve(int testNumber, MyScanner in, PrintWriter out) {
            int a = in.nextInt();
            int b = in.nextInt();
            double ans = -1;
            int left = a - b;
            int right = a + b;
            ans = mini(left, b);
            ans = Math.min(ans, mini(right, b));
            if (ans == Double.MAX_VALUE) {
                out.println(-1);
                return;
            }
            out.println(String.format("%.12f", ans));
        }

        private double mini(int val, int b) {
            if (val < 0) return Double.MAX_VALUE;
            if (val == 0) return b;
            double ans = Double.MAX_VALUE;
        /*for(int c = 2; ; c+=2){
            double x = (1.0*val)/c;
            if(x >= b) ans = x;
            else break;
        }*/
            double dval = 1.0 * val;
            long low = 1, high = Long.MAX_VALUE / 2 - 1;
            while (low <= high) {
                long mid = (low + high) / 2;
                if ((dval / mid / 2) >= b) {
                    ans = Math.min(ans, dval / mid / 2);
                    low = mid + 1;
                } else {
                    high = mid - 1;
                }
            }
            return ans;
        }

    }

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

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

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

    }
}