AbsSequence | Topcoder Archive

Problem Statement

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

S₀ = first;
S₁ = second;
S_i = |S_i-2 - S_i-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

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

"823"

"470"

{"3","1","31","0","8","29","57","75","8","77"}

Returns: {"117", "470", "2", "823", "115", "87", "49", "25", "115", "23" }

"710370"

"177300"

{"5","95","164721","418","3387","710","0","1197","19507","5848"}

Returns: {"178470", "108270", "90", "0", "90", "90", "710370", "90", "0", "0" }

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