#2331 What's the next?

33  1 s   128 MB  


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 non-zero 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 non-zero 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 non-zero integer.


Given three successive members of a sequence, you need to determine the type of the progression and the next successive member.



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.


For each test case, you program must print a single line of the form:




where XX is either AP or GP depending if the given progression is an A either an arithmetic or geometric progressions.


Sample Input

Sample Output

4 7 10
2 6 18
0 0 0
AP 13
GP 54


ACPC 2010 A