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 PYTHON):

Solution:
#In the name of God

import math
a, b = map(int, raw_input().split())
x = float("inf")

k_max = math.ceil((a+b)/(2.0*b))
k_max = max(k_max, (a-b)/(2.0*b))

x1 = (a+b)/(2.0*k_max)
x2 = (a-b)/(2.0*k_max)
k = k_max

while not (0 < b <= x1) and not (0 < b <= x2) and k >= 1:
	k-=1
	if k == 0:
		break
	x1 = (a+b)/(2.0*k)
	x2 = (a-b)/(2.0*k)


if k == 0:
	print -1
	exit()
else:
	x1 = x1 if b <= x1 else float("inf")
	x2 = x2 if b <= x2 else float("inf")

print min( x1, x2 )