def solution(pegs):
    a, b = -1, -1
    odd, even = sum_odd_even(pegs)

    if len(pegs) % 2 == 0:
        s = 2 * odd - 2 * even - pegs[-1] + pegs[0]
        if s % 3 == 0:
            a, b = 2*s/3, 1
        else:
            a, b = 2*s, 3
    else:
        s = 2 * odd - 2 * even + pegs[-1] + pegs[0]
        a, b = 2*s, 1

    if check_all_gear_size(a, b, pegs):
        return [a, b]
    return [-1, -1]

def sum_odd_even(pegs):
    odd, even = 0, 0
    for i, peg in enumerate(pegs):
        if i % 2 == 1:
            odd += peg
        else:
            even += peg
    return odd, even

def check_all_gear_size(a, b, pegs):
    if a < 2*b:
        return False

    p = list(pegs) if b == 1 else [b*p for p in pegs]

    last_peg = p[0]
    last_gear = a
    for i in range(1, len(p)):
        peg = p[i]
        gap = peg - last_peg
        if gap - last_gear < b:
            return False
        last_gear = gap - last_gear
        last_peg = peg

    return True


tests = [
        ([4, 30, 50], [12, 1]),
        ([4, 17, 50], [-1, -1]),
        ([1, 2], [-1, -1]),
        ([1, 3], [-1, -1]),
        ([1, 4], [2, 1]),
        ([1, 5], [8, 3]),
        ([1, 2, 3], [-1, -1]),
        ]

for i, o in tests:
    result = solution(i)
    print (i, result == o, result, o)