### Problem Statement

Each digit can be represented using a certain number of matches. Your goal is to create the largest possible number using the matches that you have. For example, if you need 6 matches for zero, 7 matches for one, and 8 matches for two, and you have 21 matches, the largest number you can create is 210 (8 + 7 + 6 = 21 matches).

You are given a String[] matches and a String n. The ith element (zero-indexed) of matches is the number of matches needed to represent the digit i. n is the number of matches you have. Return a String[] such that the first element is the number of digits of x (where x is the largest number that can be created), the second element contains the first 50 digits of x, and the third element contains the last 50 digits of x. If x has fewer than 50 digits, the second and third elements should each be all of x. No extra leading zeros should be added to any returned value. If n is too small to create any number, return a single zero as the number of digits and empty strings ("") as the second and third elements.

### Definition

 Class: MatchNumbersHard Method: maxNumber Parameters: String[], String Returns: String[] Method signature: String[] maxNumber(String[] matches, String n) (be sure your method is public)

### Notes

-It is not necessary to use all given matches. Some matches may be left unused.

### Constraints

-matches will contain between 1 and 10 elements, inclusive.
-Each element of matches will be an integer between 1 and 10 ^ 18 (fits in a long), inclusive, with no leading zeros.
-n will be an integer between 0 and 10 ^ 18 (fits in a long), inclusive, with no extra leading zeros.

### Examples

0)

 `{"6","7","8"}` `"21"`
`Returns: {"3", "210", "210" }`
 Example from the problem statement.
1)

 `{"1","7","8"}` `"21"`
`Returns: {"15", "100000000000000", "100000000000000" }`
2)

 `{"1","1","1","1","1","1","1","1","1","1"}` `"923372036854775807"`
```Returns:
{"923372036854775807",
"99999999999999999999999999999999999999999999999999",
"99999999999999999999999999999999999999999999999999" }```
 A lot of nines.
3)

 `{"1","923372036854775807"}` `"923372036854775807"`
`Returns: {"1", "1", "1" }`
4)

 `{"1","923372036854775806"}` `"923372036854775807"`
`Returns: {"2", "10", "10" }`
5)

 `{"1","5","10"}` `"10"`
`Returns: {"6", "100000", "100000" }`
6)

 `{"1","923372036854775807"}` `"923372036854775806"`
`Returns: {"1", "0", "0" }`
 Zero is the only digit that can be created. Note that no extra leading zeros should be added to any returned value.
7)

 `{"1", "10"}` `"1000000"`
```Returns:
{"999991",
"10000000000000000000000000000000000000000000000000",
"00000000000000000000000000000000000000000000000000" }```
 There are 999990 zeros in the created number, so its last 50 digits are all zeros.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6591

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=9991&pm=6591

gevak

#### Testers:

PabloGilberto , brett1479 , Olexiy , Andrew_Lazarev

Greedy