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:
from __future__ import division
a,b=map(int,raw_input().split())
from math import *
import sys
if b>a:
    print -1
    sys.exit()
if a==b:
    print a
    sys.exit()
def f1(x):
    global a,b
    return abs(-x+a+b)
def f2(x):
    global a,b
    return abs(x+b-a)
try:
    ans1=f1((a+b)/2.0)/floor(f1((a+b)/2.0)/b)
except:
    ans1=f1((a+b)/2.0)
try:
    ans2=f2((a-b)/2.0)/floor(f2((a-b)/2.0)/b)
except:
    ans2=f2((a-b)/2.0)
    if ans2<b:
        ans2=10**9+7
print min(ans1,ans2)