#!/usr/bin/env python3


def str_of_signal(signal):
    return ''.join(map(str, signal))

def apply_pattern(signal, offset=0):
    sums = [None] * (len(signal)-1) + [signal[-1]]
    for i in range(len(signal)-2, -1, -1):
        sums[i] = sums[i+1] + signal[i]

    i = 0 
    step = offset + 1

    while i + step < len(signal):
        n = sum(sums[i::4*step])
        n -= sum(sums[i+step::4*step])
        n -= sum(sums[i+2*step::4*step])
        n += sum(sums[i+3*step::4*step])

        signal[i] = abs(n)%10

        i += 1
        step += 1

    signal[i:] = [s % 10 for s in sums[i:]]


def phase(signal, n, offset=0):
    for i in range(n):
        apply_pattern(signal, offset)

def preproc(puzzle_input):
    return list(map(int, puzzle_input))

def partI(signal):
    signal = signal.copy()
    phase(signal, 100)
    return str_of_signal(signal[:8])

def partII(signal):
    signal = signal * 10**4
    offset = int(str_of_signal(signal[:7]))

    signal = signal[offset:]
    phase(signal, 100, offset)
    return str_of_signal(signal[:8])