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;

public class ProblemAboutPolyLine {
	private static final BufferedReader in = new BufferedReader(
			new InputStreamReader(System.in));

	public void solve() throws IOException {
		String[] s = in.readLine().split(" ");
		int a = Integer.parseInt(s[0]);
		int b = Integer.parseInt(s[1]);
		double res = 0.0;
		
		if (a < b) {
			res = -1.0;
		}
		else if (a == b) {
			res = (double) a;
		}
		else {
			double right, left;
			double r = (double) (a + b) / 2;
			double l = (double) (a - b) / 2;
			right = r / Math.floor(r / b);
			left = l / Math.floor(l / b);
			res = Math.min(left, right);
		}
		System.out.println(res);
	}
	
	public static void main(String[] args) throws IOException {
		new ProblemAboutPolyLine().solve();
	}
}