Migrated from Lutece 1051 Eggs broken

All parts of this problem, including description, images, samples, data and checker, might be broken. If you find bugs in this problem, please contact the admins.

Description

There is a building which is $n$ floors high. Bob has $K$ same eggs now. It is known that, the egg will be broken if Bob throws it from the $n_{th}$ floor. Now Alice is wondering, what's the minimum expected times Bob will throw eggs until he finds the smallest $x$, if Bob throws an egg from the $x_{th}$ floor the egg will be broken.

The $x$ is distributed in $[1, n]$ uniformly.

As is known to everyone of you, Bob loves Alice very much. Could you tell Bob the answer to help Bob leave a good impression on Alice.

Input

The first line contains two integers $n$ and $K$, which denote the number of floors and the number of eggs Bob has now.

It is guaranteed that $1 \leq n \leq 1000, 1 \leq K \leq 15$

Output

Print the minimum expected times Bob will throw eggs in one line.

The answer should be rounded to $5$ digits after the decimal point.

Samples

4 2

2.00000

Resources

The 13th UESTC Programming Contest Final