Problem Statement 
 Taro likes apples very much. He has N boxes numbered from 0 to N1. Box i contains red[i] red apples and green[i] green apples. He decided to choose one apple from his boxes, and he does so in the following way:

First Step: He chooses a nonempty subset of his N boxes randomly and transfers all apples from those boxes to another box (this is a box other than the original N boxes and it is initially empty). Each nonempty subset of boxes has the same probability of being chosen.

Second Step: He chooses one apple from the new box randomly. Each apple in the box has the same probability of being chosen.
Return the probability that Taro chooses a red apple.


Definition 
 Class:  RandomAppleEasy  Method:  theRed  Parameters:  int[], int[]  Returns:  double  Method signature:  double theRed(int[] red, int[] green)  (be sure your method is public) 




Notes 
  Your return value must have an absolute or relative error less than 1e9. 

Constraints 
  red will contain between 1 and 50 elements, inclusive. 
  red and green will contain the same number of elements. 
  Each element of red and green will be between 1 and 10, inclusive. 

Examples 
0)  
  Returns: 0.38461538461538464  There is only one box which contains 5 red apples and 8 green apples. The probability of choosing a red apple is 5 / 13. 


1)  
  Returns: 0.5888888888888888  If he chooses only box 0 in the first step, the probability of choosing a red apple is 1 / 2.
If he chooses only box 1 in the first step, the probability of choosing a red apple is 2 / 3.
If he chooses both boxes in the first step, the probability of choosing a red apple is 3 / 5.
So the probability of choosing a red apple is (1 / 2 + 2 / 3 + 3 / 5) / 3 = 53 / 90. 


2)  
 {2, 5, 6, 4, 9, 10, 6, 2}  {2, 5, 6, 4, 9, 10, 6, 2} 
 Returns: 0.4999999999999999  

3)  
 {2, 5, 6, 4, 9, 10, 6, 2}  {6, 7, 4, 5, 3, 2, 9, 1} 
 Returns: 0.5429014970733334  

4)  
 {5, 1, 2, 8, 4, 1, 1, 2, 3, 4, 5, 2, 10, 2, 6, 2, 8, 7, 9, 3}  {4, 7, 1, 1, 10, 3, 4, 1, 6, 2, 7, 6, 10, 5, 2, 9, 3, 8, 1, 8} 
 Returns: 0.46460213827476854  
