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Time Limit: 5000 MS    Memory Limit: 131072 K

Description

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.

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.

Sample Input

4 7 10
2 6 18
0 0 0

Sample Output

AP 13
GP 54

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