### Problem Statement

A juice company is running a promotion where each juice bottle they sell contains a code that you can redeem for a prize. There are n different codes, each corresponding to a different type of prize. The codes are evenly distributed, so the probability of winning a certain type of prize is 1/n for each bottle. The codes are written underneath the bottle caps, so you can't read them until you buy the bottles. Your goal is to collect k different types of prizes. Return the expected number of bottles you must buy to achieve this goal.

### Definition

 Class: CollectingBonuses Method: expectedBuy Parameters: String, String Returns: double Method signature: double expectedBuy(String n, String k) (be sure your method is public)

### Notes

-The returned value must be accurate to within a relative or absolute value of 1E-9.

### Constraints

-n and k will contain digits ('0' - '9') only.
-n and k will represent positive integers without leading zeros.
-n will represent an integer between 1 and 10^18, inclusive.
-k will represent an integer between 1 and the integer n represents, inclusive.

### Examples

0)

 `"1"` `"1"`
`Returns: 1.0`
 With only 1 type of prizes you just need to buy 1 bottle.
1)

 `"2"` `"1"`
`Returns: 1.0`
 Now there are 2 types of prizes, but any one will satisfy you, so you again need only 1 bottle.
2)

 `"2"` `"2"`
`Returns: 3.0`
 First you buy 1 bottle and collect some type of prizes. After this, you need to collect another type of prizes. Only half of bottles contains it, so in average you must buy 2 more bottles to achieve your goal.
3)

 `"4"` `"3"`
`Returns: 4.333333333333333`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8764

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=12172&pm=8764

ymatsu

#### Testers:

PabloGilberto , Andrew_Lazarev , ivan_metelsky

Math