import sys

def naive(v, i):
    if not v:
        return 0
    elif i == 0:
        return v[0]
    elif i > 0:
        return naive(v, i - 1) + naive(v[1:], i - 1)
    else:
        return naive(v, i + 1) - naive(v[1:], i)


def closed(v, i):
    s = 0;
    base = 1
    for k, x in enumerate(v):
        if k > 0:
            base *= (i - k + 1) / k
        s += x * base
    return int(s)


def get_start_values(numbers):
    diff = [numbers[i + 1] - numbers[i] for i in range(len(numbers) - 1)]
    if all(x == 0 for x in diff):
        return [numbers[0]]
    else:
        return [numbers[0], *get_start_values(diff)]


with open(sys.argv[1]) as fh:
    sum1 = 0
    sum2 = 0

    for line in fh:
        numbers = [int(s, 10) for s in line.split()]
        v = get_start_values(numbers)
        sum1 += closed(v, len(numbers))
        sum2 += closed(v, -1)

    print(f'part1: {sum1}')
    print(f'part2: {sum2}')
    print(closed([0, 0, 0, 1], 5))