# Pastebin B3jfb60h
# Extended Gray codes
# base N, length K
def gray(N,K):
    g = [0 for _ in range(K+1)]
    u = [1 for _ in range(K+1)]

    for idx in range(9): # max N**K
        print(idx,''.join(reversed([str(i) for i in g[:-1]])))
        i = 0
        k = g[0] + u[0]
        while (k >= N or k < 0):
            u[i] = -u[i]
            i += 1
            k = g[i] + u[i]
        g[i] = k

gray(3,3)