1 vs. 100 is a quiz that we could follow on TVs a few years ago. For the purposes of this task, we will slightly simplify the quiz rules.
The contestant answers questions and has to throw out
Let's say that the quiz is called
Input
In the only line there are the integer numbers
Output
Print the maximum possible amount that Mirko M. could have won divided by
Your answer will be considered correct if relative or absolute difference from the official answer is at most
Scoring
In the sample tests totally worth 15% of the points it will be true that
In the sample tests totally worth an additional 35% points it will be true that
Sample Input 1
5 3
Sample Output 1
2.100000000
Explanation for Sample Output 1
Mirko M. played against five players that he threw out in three rounds.
In order to win the maximum possible amount, firstly, he had to throw out three opponents and then two more times one at a time.
In that case, the amount won is equal to
Sample Input 2
10 10
Sample Output 2
2.928968254
Sample Input 3
100 10
Sample Output 3
4.590928516
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