P03_ACPC10A.py

# 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.
#
# Example
#
# Input:
# 4 7 10
# 2 6 18
# 0 0 0
#
# Output:
# AP 13
# GP 54

while(True):
    a, b, c = map(int, input().split())
    if a == b == c == 0:
        break
    if b-a == c-b:
        print ('AP', c + b - a)
    else:
        print ('GP', c * (b // a))