### 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 ith element of probability is the percentage chance of the ith horse winning the race, and the ith element of amounts is the amount bet on the ith 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 non-negative 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 1e-9.

### 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)

 `{30} ` `{100}` `10`
`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 70-30*P. The highest payout factor that ensures this is at least 10 is 2.
1)

 `{50,40}` `{300,200}` `100`
`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)

 `{50} ` `{100}` `1000`
`Returns: -1.0`
 Return -1 because the payout factor in this case will be negative.
3)

 `{0}` `{100} ` `100`
`Returns: -2.0`
 The payout factor is irrelevant. The company always gains 100 dollars.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=7822

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10709&pm=7822

Ishan

#### Testers:

PabloGilberto , brett1479 , Olexiy , Andrew_Lazarev

Math, Recursion