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.util.Scanner;


public class Main_Round320Div2_C {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		long a = sc.nextLong();
		long b = sc.nextLong();
		
		if (b > a) {
			System.out.println("-1");
		} else if (b == a) {
			System.out.println(a);
		} else {
			double tmp1, tmp2;
			tmp1 = Double.MAX_VALUE;
			if (a >= 3 * b) {
				tmp1 = (double)(a - b) / 2;
				tmp1 = tmp1 / (int)(tmp1 / b);
			}
			
			tmp2 = (double)(a + b) / 2;
			tmp2 = tmp2 / (int)(tmp2 / b);

			System.out.printf("%.10f\n", Math.min(tmp1, tmp2));
		}

		sc.close();
	}
}