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  
 
Notes  
  The returned value must be accurate to within a relative or absolute value of 1E9.  
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  
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