Problem Statement  
A magic arithmetic progression with k elements is a sequence of the form x, x+d, x+2*d, ..., x+(k1)*d for some positive integers x and d. How many integers between left and right, inclusive, can be represented as the sum of some magic arithmetic progression with exactly k elements?  
Definition  
 
Constraints  
  left will be between 1 and 1000000000, inclusive.  
  right will be between left and 1000000000, inclusive.  
  k will be between 2 and 5, inclusive.  
Examples  
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