### Problem Statement

A subsequence of a string s is a string that can be obtained by erasing zero or more characters from s. For example, "aacb", "c", "", and "abacaba" are subsequences of "abacaba", but "bbc" is not.

Common subsequences of strings s1 and s2 are strings that are subsequences of both s1 and s2.

A string s1 is called a cyclic shift of string s if s1 can be obtained by removing zero or more characters from the beginning of string s and appending them to the end of string s in the same order. For example, strings "abcde", "bcdea" and "eabcd" are cyclic shifts of string "abcde", but "cdeba" is not.

You are given two String[]s a and b. Construct a string A by concatenating all the elements of a, and construct a string B by concatening all the elements of b.

Consider all common subsequences for all pairs (x, y), where x is any cyclic shift of string A, and y is any cyclic shift of string B. There are length(A) * length(B) such pairs. Find the common subsequence among all of these that comes last alphabetically, and return the last suffixLength characters of that subsequence. If the subsequence contains less than suffixLength characters, then return the whole subsequence.

### Definition

 Class: CommonSubsequence Method: maxLex Parameters: String[], String[], int Returns: String Method signature: String maxLex(String[] a, String[] b, int suffixLength) (be sure your method is public)

### Constraints

-a and b will each contain between 1 and 50 elements, inclusive.
-Each element of a and b will contain between 1 and 50 characters, inclusive.
-Each element of a and b will contain only characters with ASCII value between 35 and 126, inclusive.
-suffixLength will be between 1 and 100, inclusive.

### Examples

0)

 `{"baab"}` `{"aaabb"}` `10`
`Returns: "bbaa"`
 The answer is the one of the common subsequences for the pair ("bbaa", "bbaaa").
1)

 `{"a", "cb"}` `{"bc", "a"}` `100`
`Returns: "cb"`
 The answer is one of the common subsequences for the pair ("acb", "cab") (there exist more such pairs).
2)

 `{"xzzzzzzzzzzzzzzzzzzx"}` `{"xxxxzzzzzzzzzzz"}` `10`
`Returns: "zzzzzzzzxx"`
3)

 `{"ichhbca", "aghafbbgbaehi"}` `{"jdhccgeiaaijbddh"}` `6`
`Returns: "iihhge"`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8151

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10924&pm=8151

Mike Mirzayanov

#### Testers:

PabloGilberto , radeye , Olexiy , ivan_metelsky

#### Problem categories:

Simple Search, Iteration