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 AProblemAboutPolyline {
	private AProblemAboutPolyline() throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String[] split = br.readLine().split(" ");
		int a = Integer.parseInt(split[0]);
		int b = Integer.parseInt(split[1]);

		if (b > a) {
			System.out.println(-1);
			return;
		}
		if ((a - b) % b == 0 && ((a - b) / b) % 2 == 0) {
			System.out.println(b);
			return;
		}

		int ab = a / b;
		if (ab%2 == 0)
			ab--;
		double x1 = b;
		double x2 = b + (a - ab + 0.0) / ab;
		double mid = (x1 + x2) / 2;

		while (x2 - x1 > 1e-10 && (x2-x1)/mid > 1e-10) {
			if (mid * (ab + 1) - b >= a) {
				x2 = mid;
			} else {
				x1 = mid;
			}
			mid = (x1 + x2) / 2;
		}

		System.out.println(mid);

	}

	public static void main(String[] args) throws IOException {
		new AProblemAboutPolyline();
	}
}