#! /usr/local/bin/env python3
import math

def spool(i: int):
    """
    This method takes the current stack, divides it by 5 and wastes one parcel
    :return: The number being taken, the parcels being wasted
    """
    m: int = i % 5 # The amount beeing wasted
    l = math.floor(i / 5) # The amount beeing taken
    if m == 1 and l > 0:
        return m, l
    return -1, -1

def check(n, i, p):
    """
    This method checks if the current tree is resolvable
    :param: n The current tree deph
    :param: i The current stack size
    :param: p A bool flag indicating the printing
    :return: true if it is resolvable or otherwise false
    """
    if n == 0:
        return True
    m, l = spool(i)
    if m == -1 or l == -1:
        return False
    if p:
        print("Next stack size: " + str(i - l - m) + " with " + str(m) + " parcels wasted (takes " + \
                str(l) + " parcels).")
    return check(n - 1, i - m - l, p)

def search_brute_force(maximum):
    """
    This method checks all numbers until a maximum is reached
    :param: maximum The maximum int to check
    """
    i: int = 1
    exit: bool = False
    while not exit:
        if i > maximum:
            exit = True
            print("There was no number found until " + str(maximum))
        else:
            exit = check(5, i, False)
            if exit:
                print("Found with pos " + str(i))
                check(5, i, True)
        i += 1