Xand Avião is very excited to start completing the new sticker album of the Tengo-lengo-tengo Football Federation (FFT). That is because the new FFT album works like bingo: on the day you complete it, you win a prize!
The album initially has $$$N (N \leq 2026)$$$ players licensed by the FFT. Each day, in the morning, there is a $$$P\%$$$ chance that a new player joins the album. This can only happen if there are fewer than $$$2026$$$ players in the album. After all, this is the total number of football players in the world!
Xand initially has no stickers. So every day, in the afternoon, Xand will buy a new one. The sticker is equally likely to be any player currently in the album. At that moment, if Xand has all stickers of the players that are already in the album, he immediately exchanges the album for his prize.
Xand is so excited about the prize that he can barely count the days until he completes the album. So he asked for your help to count for him: what is the expected number of days Xand will need to win the sticker album prize?
The input is a single line containing two integers, $$$N$$$ ($$$1 \leq N \leq 2026$$$) and $$$P$$$ ($$$0 \leq P \leq 100$$$).
Your output must contain a single number indicating the expected number of days Xand will need to complete the sticker album. Your answer will be considered correct if it has relative or absolute error at most $$$10^{-6}$$$ with respect to the judge's answer.
1 0
1.000000000000
2 0
3.000000000000
5 10
203.072212695099
Explanation for example 1
On the first day, it is guaranteed that no new player will be added, and Xand will get the only sticker he needs.
Explanation for example 2
It is guaranteed that no new player will be added. Therefore, Xand has probability $$$\frac{1}{2}$$$ of completing the album in $$$2$$$ days, $$$\frac{1}{4}$$$ of completing it in $$$3$$$ days, and so on. Thus, the expected value is $$$\sum_{i = 1}^{\infty} (i+1) \left(\frac{1}{2}\right)^i = 3$$$.
