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
ashish_343:
20180325 23:54:42
ac finally! use b*b=ac intead of any fraction like (b/a)=c/b Last edit: 20180326 20:12:47 

returnofsk:
20180307 06:48:34
can we take inputs and immediately print outputs? I have been trying to take all inputs first then print output.. i am new here Last edit: 20180307 06:49:18 

returnofsk:
20180307 06:27:14
https://ideone.com/baoxOK it shows WA. someone help Last edit: 20180307 06:38:43 

cherub7:
20180226 15:46:13
NOTE: we will limit ourselves to arithmetic progression whose **common difference is a nonzero integer**. Last edit: 20180226 15:46:39 

firoda:
20180217 18:43:31


quock:
20180127 05:58:41
Just have to take care 0,0,0 , nothing more to ensure. 

code_071096:
20180118 20:53:03
http://www.spoj.com/submit/ACPC10A/id=21009656


y17prashant:
20171027 21:55:46
its easy but be careful to add a space in the output between Ap and the next no. it will


vkash:
20171016 11:04:26
AC in 4th go..!!


skeladoom07:
20170908 20:22:02
AC in one GO!!!

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 