CF838F Expected Earnings

You are playing a game with a bag of red and black balls. Initially, you are told that the bag has $ n $ balls total. In addition, you are also told that the bag has probability $ p_{i}/10^{6} $ of containing exactly $ i $ red balls. You now would like to buy balls from this bag. You really like the color red, so red balls are worth a unit of $ 1 $ , while black balls are worth nothing. To buy a ball, if there are still balls in the bag, you pay a cost $ c $ with $ 0

The first line of input will contain two integers $ n,X $ ( $ 1

Print a single floating point number representing the optimal expected value. Your answer will be accepted if it has absolute or relative error at most $ 10^{-9} $ . More specifically, if your answer is $ a $ and the jury answer is $ b $ , your answer will be accepted if .

Here, there is equal probability for the bag to contain 0,1,2,3 red balls. Also, it costs 0.2 to draw a ball from the bag.