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
yomf:
20200105 06:52:30
Wrong statement, the input is not integers.


vimpyskal:
20191022 03:43:24
@moh_game_dev the problem says that the number a,b,c are distinct. 

emtiaz_001:
20190823 07:29:18
simple AC in first go!!!!!!!!! 

rock_puneet:
20190819 09:05:45
you should first check for AP condition so it treat it as AP [moh_game_dev] 

moh_game_dev:
20190721 22:37:50
1 1 1 should be AP or GP ? 

puszek215:
20190702 02:18:20
Print the answer without trailing zeros so that it's GP 54 and not GP 54.0 and GP 0.5 and not GP 0 or GP 0.500000. 

sapto1998:
20190620 17:33:24
Those who are using arithmetic mean condition,use (a+b)/2.0 instead of (a+b)/2 

itsmysyntax:
20190515 09:37:40
how to solve ?


itsmysyntax:
20190515 09:36:34
@destry_08 noone is allowed to see others solution bro 

destry_08:
20190413 16:29:55
https://www.spoj.com/submit/ACPC10A/id=23628274 can someone please tell me the problem with my code

Added by:  Omar ElAzazy 
Date:  20101130 
Time limit:  1.799s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  ACPC 2010 