Spinner Wheel#1897
A game show uses a circular spinner wheel divided into equal sectors, numbered from to . Each sector contains a question card. At the start of each round, the host spins the wheel. When the wheel stops, the question from the sector where the arrow points is selected and played. If the question from the selected sector has already been played in a previous round, the next unplayed question is chosen in the clockwise direction. The game continues until all questions have been played.
Assume that several rounds have already taken place, and questions from some sectors have already been played.
Your task is to determine the probability that in the -th round (starting from the current round), the question in the -th sector will be played. Since the wheel is balanced, the probability of the arrow stopping in any sector is equal.
The first line contains three integers , , (1 \leq i \leq N \leq 20, 1 \leq k \leq N). The second line contains numbers, each either or . A means that the question from this sector has already been played, and a means the question is still available.
Output the probability that the question from the -th sector will be played after the -th spin of the wheel, with a precision of at least 10^{-8}.
Example 1