OpenKattis
Increasing CP5 Lower Bound (Day 4)

#### Start

2020-12-09 18:10 AKST

## Increasing CP5 Lower Bound (Day 4)

#### End

2020-12-10 00:00 AKST
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# Problem FPokeball Fever

Image by succo

Pokemon Go has become a recent trend. Zapray becomes immediately addicted to the game after it comes out. Zapray’s Pokemon journey begins with a bag of $100$ Pokeballs. Each time he encounters a Pokemon, he keeps throwing Pokeballs to the Pokemon until he either catches the Pokemon or runs out of Pokeballs. Each Pokeball Zapray throws succeeds in catching the Pokemon with a constant probability $P$. If Zapray finds that he has no Pokeballs when he tries to catch a Pokemon, he gives up on that Pokemon (not catching it) and heads to the Pokeshop to buy a new bag of $100$ Pokeballs for $5$ dollars. Zapray moves on to search for his next Pokemon after he refills the Pokeballs. In particular, if Zapray successfully catches a Pokemon with his last Pokeball, he does not refill his Pokeballs until he encounters the next Pokemon and realizes that he has run out of Pokeballs.

Suppose Zapray encounters $N$ Pokemons in the next few days, what is the expected amount of money he would spend on Pokeballs?

## Input

The input has an integer $N$ ($1\leq N\leq 10^9$) and a real number $P$ ($0 \leq P\leq 1$). $P$ is given with exactly three digits after the decimal point.

## Output

Output the expected amount of money Zapray would spend on Pokeballs. Your answer is considered correct if it has an absolute or relative error of no more than $10^{-6}$ from the correct answer.

## Note

Pokemon Go was developed by Niantic, Inc. Niantic does not endorse and has no involvement with the ProgNova contest.

Sample Input 1 Sample Output 1
50 0.125

16.339203308

Sample Input 2 Sample Output 2
201 1.000

5.000000000

Sample Input 3 Sample Output 3
7 0.000

35.000000000