def cascade(n):
    """Draw a cascading tree.

    >>> cascade(486)
    486
    48
    4
    48
    486
    >>> cascade(48)
    48
    4
    48
    >>> cascade(4)
    4
    """
    if n < 10:
        print(n)
    else:
        print(n)
        cascade(n // 10)
        print(n)


def cascade_alt(n):
    """Draw a cascading tree. Alternate short implementation.

    >>> cascade_alt(486)
    486
    48
    4
    48
    486
    >>> cascade_alt(48)
    48
    4
    48
    >>> cascade_alt(4)
    4
    """
    print(n)
    if n >= 10:
        cascade_alt(n // 10)
        print(n)


def fib(n):
    """Return the nth Fibonacci number.
    
    >>> fib(0)
    0
    >>> fib(1)
    1
    >>> fib(6)
    8
    >>> fib(30)
    832040
    """
    if n == 0:
        return 0
    elif n == 1:
        return 1
    else:
        return fib(n - 2) + fib(n - 1)


def broken_fib(n):
    """Broken version of fib which is missing a base case and throws a 
    RecursionError.

    >>> broken_fib(5)
    Traceback (most recent call last):
    ...
    RecursionError: maximum recursion depth exceeded in comparison
    """
    if n == 0:
        return 0
    else:
        return broken_fib(n - 2) + broken_fib(n - 1)


def fib_iter(n):
    """Return the nth Fibonacci number. Iterative.

    >>> fib_iter(0)
    0
    >>> fib_iter(1)
    1
    >>> fib_iter(6)
    8
    >>> fib_iter(30)
    832040
    """
    i = 0
    curr, next = 0, 1
    while i < n:
        curr, next = next, curr + next
        i += 1
    return curr


def count_part(n, m):
    """Count the number of ways to give out n pieces of chocolate if 
    nobody can have more than m pieces. Both n and m are positive.
    
    >>> count_part(6, 4)
    9
    """ 
    if n == 0:
        return 1
    if n < 0:
        return 0
    elif m == 0:
        return 0
    else:
        with_m = count_part(n - m, m)
        wo_m = count_part(n, m - 1)
        return with_m + wo_m