'''
Let's grok division (and modulus.)

For now we will deal with both positive
(or at least of the same sign.)


'''

def div_mod(A, B):
    '''
    A and B are lists of digits, LSB->MSB.
    '''
    if not A:
        return [], []
    if not B:
        raise ZeroDivisionError()
    a_len, b_len = len(A), len(B)
    if a_len < b_len or (a_len == b_len and  A[-1] < B[-1]):
        return [], A

    # Whew! Okay, we got all that out of the way.
    # A > B

    A, A_digits = A[:-b_len], A[-b_len:]
    if -1 == cmp_digits(A_digits, B):
        # Because we know
        #   A > B  AND a_len >= b_len (aka len(A_digits))
        # if A_digits < B there must be at least one more
        # digit in A:
        assert a_len > b_len
        A_digits.insert(0, A.pop())
        assert -1 < cmp_digits(A_digits, B)
    q, R = lil_divmod(A_digits, B)
    # So we have divided a prefix of A by B
    # resulting in a digit q of the answer Q
    # and a remainder R that must be extended
    # with the rest of the digits of A to make
    # a new number N

    N = A + R

    # which then must either be the remainder of
    # the whole thing if N < B...
    if -1 == cmp_digits(N, B):
        return [q], N
    # Otherwise, we find the rest of the digits
    # by
    Q, R = div_mod(N, B)
    Q.append(digit)
    return Q, R

def lil_divmod(A, B):
    assert -1 < cmp_digits(A, B)
    assert A and B
    # There is a greatest digit between 0..9 such that:
    # B * digit <= A
    # The obvious thing to do here is a bisect search,
    # if we were really just doing 0..9 we could go linear.
    digit = 9
    Q = mul_digit_by_list_of_digits(digit, B)
    while 1 == cmp_digits(Q, A):
        digit = digit - 1
        if not digit:
            raise ValueError('huh?')
        Q = mul_digit_by_list_of_digits(digit, B)
    return digit, subtract(A, Q)

def mul_digit_by_list_of_digits(digit, A):
    assert 0 <= digit <= 9
    for n in A:
        assert 0 <= n <= 9
    return int_to_list(list_to_int(A) * digit)

def int_to_list(i):
    assert i >= 0
    return list(map(int, str(i)[::-1]))

def list_to_int(A):
    if not A: return 0
    i = int(''.join(map(str, A[::-1])))
    assert i >= 0
    return i

def cmp_digits(A, B):
    if len(A) > len(B):
        return 1
    if len(A) < len(B):
        return -1
    for a, b in zip(reversed(A), reversed(B)):
        if a > b: return 1
        if a < b: return -1
    else:
        return 0


def subtract(A, B):
    return int_to_list(list_to_int(A) - list_to_int(B))


##A = int_to_list(123)
##B = int_to_list(72)
##print(A, B)
##Q = mul_digit_by_list_of_digits(9, A)
##print(Q)

A = int_to_list(145)
B = int_to_list(72)

##q, R = lil_divmod(A, B)
##print(f'divmod({list_to_int(A)}, {list_to_int(B)}) = ',
##      q, list_to_int(R))

def try_it(a, b):
    A = int_to_list(a)
    B = int_to_list(b)
    Q, R = div_mod(A, B)
    print(f'divmod({list_to_int(A)}, {list_to_int(B)}) = {list_to_int(Q)}, {list_to_int(R)}')

try_it(145, 72)
try_it(1450, 72)


##print(cmp_digits([], []))
##print(cmp_digits([], [1]))
##print(cmp_digits([1], []))
##print(cmp_digits([1], [1]))
##print(cmp_digits([0,1], [1]))