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 Polyline {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int a = scanner.nextInt();
		int b = scanner.nextInt();
		scanner.close();

		if (b > a) {
			System.out.println(-1);
			return;
		}
		
		if ( b == a) {
			System.out.println(a);
			return;
		}

		int k = (a - b) / (2 * b);
		double x = a - b;
		double y = a + b;

		if (k > 0) {
			x /= 2 * k;
		} else {
			x = a;
		}
		
		y /= 2 * k + 2;
		if ( x > y ) {
			x = y;
		}
		System.out.format("%.12f\n", x);
	}

}