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:
import math
a, b = map(int, raw_input().split())

if a == b:
  print a
  exit()

def right(a, b):
  if a >= b:
    a = float(a)
    b = float(b)
    h = (b + a) / 2.0
    return h / math.floor(h / b)
  else:
    return -1
    
xR = right(a, b)
xL = right(a - 2 * b, b)

if xR != -1 and xL != -1:
  print min(xR, xL)
elif xR != -1:
  print xR
elif xL != -1:
  print xL
else:
  print -1