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
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


mgroovyank:
20190413 13:36:35
don't use fractions to check condition 

singhaditya97:
20190328 19:15:02
quite an easy problem. just keep in mind that three consecutive zeroes at the program


nothene:
20190304 11:03:47
@vambot int is fine 

vambot:
20190226 14:18:19
use float instead of int


wingman__7:
20190126 07:11:16
Those who are using Python be careful (i got a lot of errors) , use C it's an easy question btw. Last edit: 20190126 07:11:45 

aurora_prz:
20190122 01:54:28
It gives me Run Time Error. Do you have any idea why? 

mohammadsaad:
20181121 14:07:43
AC In One Go!!! Requires Some Basic Math. 
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 