### Problem Statement

An integer arithmetic progression is a sequence defined by two positive integers, p and q, where p is the first element in the sequence, and all other elements are obtained by adding q to the previous element. For example, if p = 1 and q = 2, the sequence would be: 1, 3, 5, 7, ...

An integer geometric progression is a sequence defined by two positive integers, p and q, where p is the first element in the sequence, and all other elements are obtained by multiplying the previous element by q. For example, if p = 3 and q = 2, the sequence would be: 3, 6, 12, ...

You are given a int[] A, which contains either an integer arithmetic or geometric progression. Determine which one it is and return the next element in the sequence. It is guaranteed that A will uniquely represent either an arithmetic or geometric progression and that result will fit in a 32-bit signed integer.

### Definition

 Class: GuessingNextElement Method: guess Parameters: int[] Returns: int Method signature: int guess(int[] A) (be sure your method is public)

### Constraints

-A will contain between 3 and 50 elements, inclusive.
-Each element of A will be between 1 and 10^6, inclusive.
-A will be sorted in ascending order.
-A will uniquely represent either an arithmetic or geometric progression.

### Examples

0)

 `{364,843,1322,1801}`
`Returns: 2280`
 This sequence represents an arithmetic progression where p = 364 and q = 479. The next element is 1801 + 479 = 2280.
1)

 `{394,1172,1950,2728,3506,4284,5062,5840}`
`Returns: 6618`
2)

 `{13,117,1053,9477,85293}`
`Returns: 767637`
 This sequence represents a geometric progression where p = 13 and q = 9. The next element is 85293 * 9 = 76737.
3)

 `{22,220,2200,22000}`
`Returns: 220000`
4)

 `{250000, 500000, 1000000}`
`Returns: 2000000`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8539

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=11121&pm=8539

Relja

#### Testers:

PabloGilberto , Olexiy , marek.cygan , ivan_metelsky

#### Problem categories:

Simple Search, Iteration