def normalForm (x, b):
    if x < b:
        return x
    L = []
    e = 0
    while x > 0:
        m = x % b
        if m > 0:
            L.append([normalForm(e, b), m])
        x //= b
        e += 1
    return L

def fromNormalForm (L, b):
    if type(L) is int:
        return L
    return sum(f * b**fromNormalForm(e, b) for e, f in L)

from re import match

def maybeAddParens (s):
    return s if match(r"^[0-9]+$", s) else "(" + s +")"

def beautify (f, b, e):
    if e == 0:
        return str(f)
    if e == 1:
        if f == 1:
            return str(b)
        else:
            return "{}*{}".format(f, b)
    if f == 1:
        return "{}^{}".format(b, maybeAddParens(normalFormToString(e, b)))
    return "{}*{}^{}".format(f, b, maybeAddParens(normalFormToString(e, b)))

def normalFormToString (L, b):
    if type(L) is int:
        return str(L)
    return "+".join(beautify(f, b, e) for e, f in L)

def goodstein (x, n):
    b = 2
    while b <= n + 1:
        if x == 0:
            break
        N = normalForm(x, b)
        print("{} = {}".format(x, normalFormToString(N, b)))
        b += 1
        x = fromNormalForm(N, b) - 1

goodstein(13, 7)

goodstein(7, 13)