### Problem Statement

You are taking your car on a long trip and have only a limited amount of fuel. You know how many liters of fuel your car uses per hour for certain speeds and you'd like to know how far a certain amount of fuel will take you when travelling at the optimal speed.

You will be given a int[] velocities and a int[] consumptions. velocities specifies a number of velocities in kilometers per hour. The ith element of consumptions is the amount of fuel (in milliliters) the car will consume in 1 hour, if your speed is equal to the ith element of velocities. In addition, you will be given an int fuel specifying the total amount of fuel in milliliters. Your method should return a double, equal to the maximum distance that the car can travel (in kilometers) with the given amount of fuel, and travelling at a constant velocity equal to one of the elements of velocities.

### Definition

 Class: FuelConsumption Method: maximalDistance Parameters: int[], int[], int Returns: double Method signature: double maximalDistance(int[] velocities, int[] consumptions, int fuel) (be sure your method is public)

### Notes

-The returned value must be accurate to within a relative or absolute value of 1E-9.

### Constraints

-velocities and consumptions will contain the same number of elements.
-velocities and consumptions will each contain between 1 and 50 elements, inclusive.
-Each element of velocities will be between 5 and 250, inclusive.
-Each element of consumptions will be between 1000 and 20000, inclusive.
-fuel will be between 100 and 50000, inclusive.
-velocities will not contain duplicate elements.

### Examples

0)

 `{100}` `{10000}` `10000`
`Returns: 100.0`
 At 100 km/hour, you consume 10 liters of fuel per hour. You have 10 liters, so you can cover 100 kilometers.
1)

 `{70, 80, 90, 100, 60, 110}` `{4000, 4000, 4000, 4000, 4000, 4000}` `40000`
`Returns: 1100.0`
 Here, your car consumes the same amount of fuel at different velocities. In such cases the faster you drive the further you go.
2)

 `{250, 240, 230, 220, 210, 211}` `{5000, 4500, 4000, 3500, 3000, 3000}` `50000`
`Returns: 3516.6666666666665`
3)

 `{5, 10, 20, 40, 80}` `{1000, 2500, 6250, 9000, 18000}` `47832`
`Returns: 239.16`
4)

 `{5, 10, 20, 40, 80, 160}` `{1000, 2500, 6250, 8000, 9500, 20000}` `47832`
`Returns: 402.79578947368424`
5)

 ```{240, 195, 130, 133, 15, 160, 111, 206, 72, 149, 146, 115, 235, 183, 102, 96, 163, 61, 196, 52, 87, 139, 33, 7, 90, 67, 118, 227, 197, 114}``` ```{14837, 2981, 17292, 18591, 4832, 7461, 17991, 18369, 18291, 9400, 15179, 3317, 2595, 2441, 6936, 8028, 14973, 18981, 12503, 7816, 2883, 6385, 6230, 18157, 16567, 9310, 2866, 4687, 14171, 4477}``` `31710`
`Returns: 2871.6184971098264`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=2980

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=5863&pm=2980

Olexiy

#### Testers:

PabloGilberto , lbackstrom , brett1479

#### Problem categories:

Brute Force, Simple Math