DotA Quals#9114
Today, instead of preparing for the upcoming exams, a student with the nickname Idned decided to participate in the open qualification of a major DotA (Development of the Algorithms) tournament. The qualification is conducted as a single-elimination tournament with 2^n participants, and Idned is one of them. A total of rounds will be held.
In each round, all remaining participants are randomly paired, with all possible pairings equally likely. In each pair, the participants play against each other, and the loser is eliminated from the tournament (and will not participate in subsequent rounds).
Each participant has a unique rating, and Idned's rating is the -th highest among all participants. Idned is confident that the outcome of each game is entirely determined by the participants' ratings: the player with the higher rating always wins.
Using this assumption, determine the expected number of rounds in which Idned will participate.
Two integers and k~(1 \le n \le 10, 1 \le k \le 2^n) — the total number of rounds and Idned's position in the overall ranking.
Print the expected number of rounds in which Idned will participate. The answer should be output with decimal places.
Example 1
Example 2