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(b>a):
	print "-1"
elif(a==b):
	print a
else:
	v1=((a+b)/b)
	if v1%2==1:
		v1=v1-1
	v2=((a-b)/b)
	if v2%2==1:
		v2=v2-1
	ans1,ans2=10**125,10**155
	if v1!=0:
		ans1=(((float)(a+b))/(v1))
	if v2!=0:
		ans2=(((float)(a-b))/(v2))
	print '%.9f' %min(ans1,ans2)