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.

-----Examples-----
Sample Input 1:
50 0.125
Sample Output 1:
16.339203308

Sample Input 2:
201 1.000
Sample Output 2:
5.000000000

Source: kattis | Difficulty: HARD


Solutions: