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 PYTHON3):

Solution:
#import sys
#sys.stdin = open("python/in", "r")
#from collections import defaultdict
#import numpy as np
#import array as rr
#arr = rr.array('q')
import math
#n = int(input())
x, y = [int (i) for i in input().split(" ")]
fail = False
if x < y:
    fail = True
    
if not fail:
    a = (x + y)/2
    ans = math.floor(a / y)
    ans = a / ans
    print (ans)
else:
    print(-1)