import numpy

def solution(n, b):
    k = len(n)
    memo = {}
    index = 0
    search = True
    while search:
        x, y, z = get_x_y_z(n, k, b)
        if x in memo:
            print(memo)
            return index - memo[x]
        memo[x] = index
        n = z
        index+=1

def get_x_y_z(n, k, b):
    pre_x = ''.join(sorted(n, reverse=True))
    x = int(pre_x, b)
    y = int(pre_x[::-1], b)
    z = numpy.base_repr(x-y, base=b).rjust(k, '0')
    return x, y, z

tests = [
        ['1211', 10],
        ['210022', 3],
        ['01', 2],
        ['10', 2],
        ['111111111', 2],
        ['999999999', 10],
        ]

for test in tests:
    print(test, solution(test[0], test[1]))