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

rv404674:
20161123 00:04:55
625 125 5 can,t be a test case because it,s common ratio is not an integer


esshuvo:
20161023 17:20:45
a,b,c mus be distinct,read the problem :) So,1,1,1 obviously not in the test case .


goutam1511:
20161003 13:52:11
can anybody give me some corner cases? 

harishdatla:
20160929 08:56:50
Why 1 1 1 should be AP while clearly above it stated that difference should be a non zero integer, anyway i guess its not in test case.. :) Last edit: 20160929 09:04:57 

hacker_sk:
20160925 20:04:29
enjoy :) Last edit: 20160925 20:07:33 

devilking:
20160916 16:55:25
common ratio should be integer


narutohokage_1:
20160807 10:28:19
1 1 1 can never be case because all three numbers should be distinct. 

mishra_sharad:
20160806 08:04:10
I haven't seen such a stupid question on spoj til date... 

sainath123456:
20160803 20:14:00
note 1 1 1 can be both ap and gp

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 