## COCI '18 Contest 4 #5 Akvizna

View as PDF

Points: 30 (partial)
Time limit: 0.75s
Memory limit: 256M

Problem type

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 people who compete against him. Everyone responds to the same question in each round and those who answer the question wrong are thrown out. The amount of money that a competitor who manages to throw out all opponents gets is equal to the sum of money won per round. In each round, all opponents are worth equally and all opponents combined are worth kunas (Croatian currency). The amount earned in a round is equal to the sum of the values of people who have been thrown out in that round. For example, if there are opponents at some point, each of them is worth kunas, and the contestant will get kunas if he or she manages to throw out opponents in that round.

Let's say that the quiz is called vs. (i.e. the competitor competes against people) and that Mirko M. managed to throw all the opponents in exactly rounds. What is the maximum amount he could have won?

#### Input

In the only line there are the integer numbers and , the numbers from the task description.

#### 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 kunas.

#### Sample Input 2

10 10

#### Sample Output 2

2.928968254

#### Sample Input 3

100 10

#### Sample Output 3

4.590928516