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 string,itertools,fractions,heapq,re,array,bisect
#from math import *
#from collections import Counter
from copy import deepcopy
def rl(s): return xrange(len(s))


INF = 2147483647


import sys
stdin = sys.stdin

a, b = map(int, stdin.readline().strip().split())

if b > a:
    print -1
elif (a - b) % (2 * b) == 0:
    print b
else:
    n = (a - b) / (2*b)
    print (b + a) / (2.0 * (n+1) )