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
rishisingh7012:
20211120 13:55:20
Cakewalk 

rohan70970:
20211118 10:25:17
Ac in one go..


drakeramory_18:
20211114 12:09:36
input method is bit diff good problem btw..


iseng_cuk:
20211016 08:39:41
<snip>


sid15298:
20210620 09:56:29
Solved problem in one go 

unwanted_coder:
20210524 19:08:07
why this give wrong ans (a+c)/2==b in if condition 

ahmedsergany:
20210206 08:03:24
AC IN ONE GO !!


aniket_s_k:
20201128 11:29:14
why this gives wrong answer when we use if(b==(a+c)/2 )? 

ghost_of_past:
20201113 19:52:39
who says float? IT JUST INTEGERS! 

karlo_2107:
20201103 19:48:39
try with bfs! 
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 