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 non-zero 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 non-zero 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 non-zero 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

Added by:Omar ElAzazy
Date:2010-11-30
Time limit:1.799s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACPC 2010

hide comments
2015-01-10 14:59:00 Raj Kumar Chauhan
do we have to consider increasing decreasing series both?
2015-01-06 23:46:59 Aseem Arora
I tried to submit the solution in both c and c++ but it shows an error everytime saying that these languages are only available in cube cluster .But if you see the all submissions page , there are accepted solutions written in these languages.I am confused by this . Can anyone please explain ?
2015-01-05 19:14:16 Ravin
AP- difference is same
GP - ratio is same
easy..
2015-01-04 14:07:01 Abhishek Naik
So how did Raman Nv submit the answer then?
2015-01-04 12:07:25 Rahul
Same Problem occurred to me as well :"Pyramid Cluster is unavailable"
2015-01-04 09:30:50 Abhishek Naik
As per SPOJ, its Pyramid cluster server is deprecated. In line with this, I'm unable to submit my solution since it is displaying "Pyramid Cluster is unavailable" message. How did the others get it submitted then? That too just a few days before?
2015-01-02 14:15:39 Raman Nv
Finally got it after outputting as GP when x=y=z!! :'D
2014-12-07 08:52:32 puts #{Jagpreet Singh Sasan}
why am i getting wrong answer???
here is my code

(reply by Min_25)
Please see the Notes below.

Notes:
> 1. Don't post any source code here.
> 3. For more discussion (hints, ideas, solutions) please visit our forum.

Last edit: 2014-12-07 09:25:59
2014-12-06 13:47:28 Deepak Thukral
4,2,1 : Next term should be 0.5 or 0.
if 0.5 then can it be 0.500000 or we have to restrict ourselves to 0.5.

--ans(Francky)--> Description is clear about that : "For this problem, we will limit ourselves to geometric progression whose common ratio is a non-zero integer."

Last edit: 2014-12-06 16:21:06
2014-12-06 12:43:24 Deepak Thukral
If the series is both AP and GP, then what we should print the series AP or GP?
eg: 2, 2, 2

--ans(Francky)--> Description is clear about that : "For this problem, we will limit ourselves to arithmetic progression whose common difference is a non-zero integer."

Last edit: 2014-12-06 13:26:35
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