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
mondalsourav:
20170215 22:49:23
only a game of data types and PROPER "ifelse" conditions. :) 

vanvinhbk94:
20170215 15:20:06
while(a!=0  b!=0  c!=0) 

arpan888:
20170211 11:32:05
How to store input ? 

giriprasad kemburu:
20170127 12:06:25
Easy Problem.Careful with Division By Zero.


sheteyash:
20170119 05:50:01
Do we have to take all the inputs first or is it okay to print an answer after every test case???My logic is correct but still giving wrong answer 

sushanth_r:
20170110 14:49:33
AC in 1st Attempt :)


rathan1999:
20161228 20:19:08
Check for Gp in if condition


suryansh_97:
20161214 06:57:33
very easy .....just check any case involving 0 ie 0 2 4


darpanjbora:
20161212 11:00:10
Finally AC after 4 WA.


bhaskar_uoh:
20161204 11:53:30
*No need to stress on data type all ints, costed me 4 WAs :( 
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 