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:
### TEMPLATE BEGIN

from collections import defaultdict

def read_int():
    return int(raw_input())

def read_ints():
    return (int(x) for x in raw_input().split())

def read_int_list():
    return [int(x) for x in raw_input().split()]

def read_float():
    return float(raw_input())

def read_floats():
    return (float(x) for x in raw_input().split())

def read_float_list():
    return [float(x) for x in raw_input().split()]

def read_list():
    return [x for x in raw_input().split()]

### TEMPLATE END

def solve():
    a, b = read_floats()
    if b > a:
        print -1
        return
    print (a+b)/(2*(int(a+b)/int(2*b)))

qq = 1
# qq = 2**30
# qq = read_int()
for _________ in xrange(qq):
    solve()