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

ghost_wire:
20160419 19:16:00
one silly mistake costed me 4 WA. 

chandansirola:
20160419 16:16:05
Last edit: 20160419 16:18:33 

ghost_wire:
20160327 10:54:26
@laid_to_rest its GP. 

Kyle Dencker:
20160315 03:44:16
very upset with myself. 3 WA because my logic on my loop was broken. 

devilshashank:
20160306 09:20:00
got wrong answer 4 times just couz ...was not giving '\n' don't forget ! 

rishabh_1997:
20160211 08:05:35
pretty easy question...ac after a silly mistake caused 1 wa


deepukps:
20151229 10:06:11
@laid to rest answer will be GP 

Siddhartha Gairola:
20151226 15:18:12
Easy just use 2*b = (a+c) 

vishu_100:
20151225 20:37:27
dont forget the /n costed me one 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 