|
Matcom Online Grader
Faculty of Mathematics and Computer Science of University of Havana
ℹ️ We've recently migrated MOG to a new server with a different grader. As a result, some features—especially those related to submission evaluation—might not work correctly. If you encounter any issues, please report them by clicking the exclamation icon in the bottom right corner of the website.
Randy is playing a simple game called "Guess the Number": there is a hidden integer $V$ whose value is between $1$ and $N$. The goal of the game is to guess this number $V$. In each round, Randy picks an integer between $1$ and $N$ as his guess. If the guess matches $V$, the game ends and he wins a prize. Otherwise, the game continues and asks Randy for his next guess, and so on.
In each round, Randy will use the following strategy to make his guess:
- He randomly selects an integer $x$ between $1$ and $N$.
- If $x$ was not tried in any previous round, $x$ would be his guess in the current round. This guess costs him \$1.
- Otherwise, as the guess in the current round, he would pick the smallest not tried integer that is larger than $x$ (but not larger than $N$). This guess also costs him \$1.
- If no such number exists, he discards $x$ and goes to step $1$. Discarding number $x$ has no cost for Randy.
Question: what is the average amount of money Randy has to pay before he wins the prize?
Input
The input consists of a single line containing two integers $N$ $(1 \le N \le 20)$ and $V$ $(1 \le V \le N)$.
Output
Output a single line with the answer to the question described above. Your answer is considered correct if its (absolute or relative) difference from the expected answer is at most $10^{-6}$.
Sample test(s)
Input
2 2
Output
1.5
Input
3 2
Output
1.944444444
Input
10 6
Output
5.305939329