Strasse

You're playing a generalized version of poker called  $(n,k)$-poker. A game of $(n,k)$-poker consists of $k$ rounds. In each round, an integer between 1 and $n$ is picked independently and uniformly at random. You can then do one of the two things: either take this number, or skip it, and then the round ends.

You must take exactly three numbers, and you win if those three numbers form a straight --- an arithmetic progression --- after reordering them somehow. What is the probability of achieving this goal if you play optimally?

The only line of the input file contains two space-separated integers $n$ and $k$, $1 \le n \le 10000$, $3 \le k \le 10000$.

Print one floating-point number: the probability of winning in $(n,k)$-poker if you play optimally. Your output will be considered correct if it differs from the answer by at most $10^{-7}$.

Three numbers form an arithmetic progression in some order if and only if one of the numbers is the average of the other two.