Problem Description

Given two integers $ N $ and $ K $.

Consider a machine that selects one integer between $ 1 $ and $ N $ (inclusive) with equal probability.

When this machine is operated three times, find the probability that the median of the three selected numbers is $ K $.

Input Format

The input is given from the standard input in the following format:

$ N $ $ K $

The first line contains two integers $N(1\ ≦\ N\ ≦\ 10^6)$ and $K(1\ ≦\ K\ ≦\ N)$ separated by a space.

Output Format

Output the probability that the median is $ K $. The output should be to the standard output, followed by a newline.

The answer will be considered correct if the absolute or relative error is within $ 10^{-9} $.

Sample Input and Output

Sample Input #1

3 2

Sample Output #1

0.48148148148148148148

Sample Input #2

3 1

Sample Output #2

0.25925925925925925926

Sample Input #3

765 573

Sample Output #3

0.00147697396984624371

Notes/Hints

Sample Explanation 1

The median is $ 2 $ when the outputs (first output, second output, third output) are:
- (1, 2, 3)
- (1, 3, 2)
- (2, 1, 3)
- (2, 3, 1)
- (3, 1, 2)
- (3, 2, 1)
- (1, 2, 2)
- (2, 1, 2)
- (2, 2, 1)
- (3, 2, 2)
- (2, 3, 2)
- (2, 2, 3)
- (2, 2, 2)

The probability of any of these occurring is $13/27\ =\ 0.481481481...$

见题面 Input 部分

见题面 Output 部分