ACPC10A  What’s Next
According to Wikipedia, an arithmetic progression (AP) is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13, . . . is an arithmetic progression with common difference 2. For this problem, we will limit ourselves to arithmetic progression whose common difference is a nonzero integer.
On the other hand, a geometric progression (GP) is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed nonzero number called the common ratio. For example, the sequence 2, 6, 18, 54, . . . is a geometric progression with common ratio 3. For this problem, we will limit ourselves to geometric progression whose common ratio is a nonzero integer.
Given three successive members of a sequence, you need to determine the type of the progression and the next successive member.
Input
Your program will be tested on one or more test cases. Each case is specified on a single line with three integers (−10, 000 < a1 , a2 , a3 < 10, 000) where a1 , a2 , and a3 are distinct.
The last case is followed by a line with three zeros.
Output
For each test case, you program must print a single line of the form:
XX v
where XX is either AP or GP depending if the given progression is an Arithmetic or Geometric Progression. v is the next member of the given sequence. All input cases are guaranteed to be either an arithmetic or geometric progressions.
Example
Input:
4 7 10
2 6 18
0 0 0
Output:
AP 13
GP 54
hide comments
cnexans:
20160726 05:32:26
Take care of the size of those numbers, you'll probably run out of time if your code is greedy enough. GL 

vishakha94:
20160719 22:21:50
Unable to understand the issue.. checked test cases still wrong answer. 

nikunjsoni:
20160719 14:21:13
should be in tutorial 

alphastar:
20160715 07:53:01
Remember 0,2,4 is a valid case ;)


Saurabh Uttam:
20160702 10:22:08
be careful with loop logic 

nis_bar10:
20160620 00:37:42
check for 4 2 1 

flyingduchman_:
20160611 20:22:25
Should be moved to tutorial. 

ujjwalverma:
20160602 19:34:30
2*b=a+c will give WA in case involving 0


s1998:
20160522 13:12:46
Last edit: 20160522 13:14:09 

ghost_wire:
20160419 19:16:00
one silly mistake costed me 4 WA. 
Added by:  Omar ElAzazy 
Date:  20101130 
Time limit:  1.799s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  ACPC 2010 