Problem Statement 
 Fox Jiro and Haruko play a game with two piles of cards: pile A and pile B. Pile A and pile B contain same number of cards. Each card contains a real number between 1.0 and 100.0. Initially, the two players have 0 points. Then they repeat following operations exactly k times:
 They choose two cards from the piles (one from pile A and another from pile B).
 The choosen cards are removed from the piles.
 Jiro earns max{a+b, a*b} points and Haruko earns min{a+b, a*b} points (where a and b are the numbers written on the two cards that were removed).
You are given a double[] pileA, a double[] pileB, and an int k. Return the maximal possible value of (Jiro's points) / (Haruko's points). 

Definition 
 Class:  FoxCardGame  Method:  theMaxProportion  Parameters:  double[], double[], int  Returns:  double  Method signature:  double theMaxProportion(double[] pileA, double[] pileB, int k)  (be sure your method is public) 




Notes 
  The returned value must have an absolute or relative error less than 1e9. 

Constraints 
  pileA and pileB will contain between 1 and 50 elements, inclusive. 
  pileA and pileB will contain the same number of elements. 
  Each element of pileA and pileB will be between 1.0 and 100.0, inclusive. 
  k will be between 1 and the number of elements in pileA, inclusive. 

Examples 
0)  
  Returns: 1.7692307692307692 
 Choosing cards with numbers 3 and 6, Jiro earns 3*6 = 18 points and Haruko earns 3+6 = 9 points.
 Choosing cards with numbers 1 and 4, Jiro earns 1+4 = 5 points and Haruko earns 1*4 = 4 points.
So the solution is (18+5) / (9+4) = 1.769230... 


1)  
 {1.234, 5.678, 9.012, 3.456, 7.89}  {2.345, 6.789, 9.876, 5.432, 1.012}  3 
 Returns: 4.159424420079523  

2)  
 {1, 1.1, 1.2, 1.3, 1.4, 1.5}  {5, 10, 15, 20, 25, 30}  2 
 Returns: 1.3972602739726028  

3)  
 {85.302, 92.798, 76.813, 37.994, 36.737, 98.659}  {13.352, 7.3094, 54.761, 8.2706, 63.223, 37.486}  3 
 Returns: 33.58603889836175  
