AT_abc469_e [ABC469E] Pro Exam Eligibility

You are given a string $ S $ of length $ N $ consisting of `o` and `x`. It is guaranteed that $ S $ contains at least $ K $ occurrences of `o`. Takahashi played a certain game $ N $ times. In the $ i $ -th game, he won if the $ i $ -th character of $ S $ is `o`, and lost if it is `x`. Takahashi chooses a pair of integers $ l $ and $ r $ satisfying the following conditions. - $ 1 \leq l \leq r \leq N $ - He won at least $ K $ times in the games from the $ l $ -th through the $ r $ -th. Find the maximum possible value of the win rate in the games from the $ l $ -th through the $ r $ -th.

The input is given from Standard Input in the following format: > $ N $ $ K $ $ S $

Output the answer in one line. Answers with an absolute or relative error of at most $ 10^{-6} $ from the true answer will be accepted.

### Sample Explanation 1 Choosing $ (1,6) $ as $ (l,r) $ gives a win rate of $ \frac{2}{3} $ . It is impossible to make the win rate larger than this while satisfying the conditions. ### Constraints - $ 1 \leq K \leq N \leq 10^6 $ - $ N $ and $ K $ are integers. - $ S $ is a string of length $ N $ consisting of `o` and `x`. - $ S $ contains at least $ K $ occurrences of `o`.