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
rish__01:
20200920 18:35:56
i got the logic of the AP GP but I keep getting the while loop condition wrong. The series is quite simple Last edit: 20200920 18:38:06 

aditigedam:
20200824 13:06:54
1. "common ratio is a nonzero integer" don't believe at this think beyond this..


singhar:
20200821 05:32:56
for input 5 0 0 output should be 0.


taran9873:
20200810 09:48:56
be careful with while loop terminating condition! 

foxface_ap:
20200529 20:18:53
Why this gives WA when we use (a+c)/2 == b as if condition?


mahabir10:
20200523 12:14:35
My 51th Problem 

landi58:
20200430 14:57:40
1. Take Float data type


codinggeek719:
20200415 23:28:22
inputs are integers as stated in question 

shammya:
20200328 04:03:21
The most easy problem in the known universe !


yomf:
20200105 06:52:30
Wrong statement, the input is not integers.

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 