Problem Statement 
 Your company runs a horse race betting service. Each person bets on a horse, and if that horse wins outright (i.e., it wins alone and doesn't tie for the win with any other hose), the person will win back their money plus a multiple of the amount they bet. This multiple is called a payout factor. In all other cases your company keeps the money. You are given a int[] probability and a int[] amounts. The i^{th} element of probability is the percentage chance of the i^{th} horse winning the race, and the i^{th} element of amounts is the amount bet on the i^{th} horse.
These probabilities are independent (see example 1 for clarification).
Return the highest payout factor such that the expected earnings of the company is minimumMoney or higher. If you can not achieve minimumMoney with a nonnegative payout factor, then return 1. If you can achieve minimumMoney with any payout factor, then return 2. 

Definition 
 Class:  RaceManagement  Method:  getPayoutFactor  Parameters:  int[], int[], int  Returns:  double  Method signature:  double getPayoutFactor(int[] probability, int[] amounts, int minimumMoney)  (be sure your method is public) 




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

Constraints 
  probability will contain between 1 and 5 elements, inclusive. 
  Each element of probability will be between 0 and 100, inclusive. 
  Each element of amounts will be between 0 and 1000, inclusive. 
  amounts will contain the same number of elements as probability. 
  The sum of all the elements in probability will be at most 100. 
  minimumMoney will be between 0 and 1000, inclusive. 

Examples 
0)  
  Returns: 2.0  Horse 1 has a 30% chance of winning. If it wins, the company has to pay out 100*P dollars, where P is the payout factor, and if it doesn't win, the company gains 100 dollars. Thus, the expected earnings of the compay is 7030*P. The highest payout factor that ensures this is at least 10 is 2. 


1)  
  Returns: 2.076923076923077  Horse A has a 50% chance of winning and horse B has a 40% chance of winning. But this also means that there is a 20% chance they tie and a remaining 30% chance neither of them wins.
Thus, in this scenario, 4 cases arise
Horse A wins 30% chance => The company loses 300*P dollars and gains 200 dollars
Horse B wins 20% chance => The company loses 200*P dollars and gains 300 dollars
Horse A & B both win (tie) 20% chance => The company loses 0*P dollars and gains 500 dollars
Neither Horse A nor horse B wins (No result) 30% chance => The company loses 0*P dollars and gains 500 dollars
To ensure the expected earnings are at least 100, the payout factor P can be at most approximately 2.077. 


2)  
  Returns: 1.0  Return 1 because the payout factor in this case will be negative. 


3)  
  Returns: 2.0  The payout factor is irrelevant. The company always gains 100 dollars. 

