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.math.*;
import java.util.Scanner;
public class Main {
	public static final double eps = 1e-10;
	public static void main(String[] args) {
		Scanner cin = new Scanner(System.in);
		double a, b;
		a = cin.nextDouble();
		b = cin.nextDouble();
		if(a == b) {
			System.out.printf("%.10f\n", a);	
		}
		else if(b > a) {
			System.out.printf("-1\n");
		}
		else {
			double k1 = a - b;
			double k2 = a + b;
			int c1 = (int)(Math.floor(k1 / (b * 2)) + eps);
			int c2 = (int)(Math.floor(k2 / (b * 2)) + eps);
			System.out.printf("%.10f\n", Math.min(k1 / c1 / 2, k2 / c2 / 2));
		}
		
	}
}