### Problem Statement

Let's consider an infinite sequence S of non-negative integers defined as follows:

S0 = first;

S1 = second;

Si = |Si-2 - Si-1| for all i >= 2.

You will be given Strings first and second, representing the 0-th and the 1-st elements of the sequence S, and a String[] indices, each element of which represents a non-negative integer without extra leading zeros. Return a String[] containing as many elements as indices, where the i-th element is equal to the indices[i]-th element of the sequence S (index is 0-based). No element of the return should contain extra leading zeros.

### Definition

 Class: AbsSequence Method: getElements Parameters: String, String, String[] Returns: String[] Method signature: String[] getElements(String first, String second, String[] indices) (be sure your method is public)

### Constraints

-first will represent an integer between 0 and 10^18, inclusive, with no extra leading zeros.
-second will represent an integer between 0 and 10^18, inclusive, with no extra leading zeros.
-indices will contain between 1 and 50 elements, inclusive.
-Each element of indices will represent an integer between 0 and 10^18, inclusive, with no extra leading zeros.

### Examples

0)

 `"21"` `"12"` `{"0", "1", "2", "3", "4"}`
`Returns: {"21", "12", "9", "3", "6" }`
 Here S0=21 and S1=12. The next three sequence elements are S2 = |21 - 12| = 9, S3 = |12 - 9| = 3 and S4 = |9 - 3| = 6.
1)

 `"0"` `"0"` `{"1000000000000000000"}`
`Returns: {"0" }`
 Here we get the sequence consisting of only zeros.
2)

 `"823"` `"470"` `{"3","1","31","0","8","29","57","75","8","77"}`
`Returns: {"117", "470", "2", "823", "115", "87", "49", "25", "115", "23" }`
3)

 `"710370"` `"177300"` `{"5","95","164721","418","3387","710","0","1197","19507","5848"}`
`Returns: {"178470", "108270", "90", "0", "90", "90", "710370", "90", "0", "0" }`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8178

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10785&pm=8178

ivan_metelsky

#### Testers:

PabloGilberto , Yarin , Olexiy

#### Problem categories:

Math, Simple Search, Iteration