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:
a, b = map(int, raw_input().split())
if a < b:
	print -1
	exit()
elif a == b:
	print "%.20f" % a
	exit()

l = 0
r = 10 ** 18
while r - l > 1:
	m = (l + r) / 2
	if b * m * 2 <= a + b:
		l = m
	else:
		r = m
if l > 0:
	ans1 = float(a + b) / 2.0 / l
else:
	ans1 = 10 ** 18

l = 0
r = 10 ** 18
while r - l > 1:
	m = (l + r) / 2
	if b * m * 2 <= a - b:
		l = m
	else:
		r = m
if l > 0:
	ans2 = float(a - b) / 2.0 / l
else:
	ans2 = 10 ** 18

ans = min(ans1, ans2)
if ans == 10 ** 18:
	print -1
else:	
	print "%.30f" % ans