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 PYTHON3):

Solution:
def main(a,b):
	if b > a:
		return(-1)
	# ver1 
	k1 = (a - b) // (2*b)
	if k1 > 0:
		x1 = (a - b) / (2 * k1)
	else:
		x1 = 10**9
	k2 = (a + b) // (2*b)
	x2 = (a + b) / (2*k2)

	return min(x1, x2)



a,b = list(map(int, input().split()))
print(main(a,b))