What? Where? When?
In the popular TV game show "What? Where? When?", a team of experts competes against TV viewers who send in questions. These questions are placed in envelopes on a round table, divided into N equal sectors, with one envelope per sector. At the center of the table is a spinning top with an arrow. Each round begins with the host spinning the top. When the top stops, the envelope in the sector where the arrow points is selected, and the host reads the question for the experts to answer after a minute of discussion. If the question from the chosen sector has already been played in a previous round, the next unplayed question in a clockwise direction is selected. Typically, the show continues until one team reaches a certain number of points, but for this problem, assume the game ends only when all questions have been played.
Assume several rounds have already occurred, and questions from some sectors have been played. "And now, attention to the question!" (gong sound!)
Your task is to determine the probability that in the k-th round (starting from the current round), the question in the i-th sector will be played. Since all sectors are identical, the probability of the arrow stopping in any sector is equal.
Input
The first line contains three integers N, i, k (1 ≤ i ≤ N ≤ 20, 1 ≤ k ≤ N). The second line contains N numbers, each either 0 or 1. A 0 indicates that the question from that sector has already been played, while a 1 means the question is still available.
Output
Output the probability that the question from the i-th sector will be played after the k-th spin of the top, with a precision of at least 10^{-8}.