De Bruijn Cycle High

A de Bruijn cycle of order $n$ for the set D = \{0, 1, \ldots, b-1\} is a cyclic sequence a_0, a_1, \ldots, a_{l-1} such that every possible vector of length $n$ over the set $D$ appears exactly once in this sequence. That is, for any sequence b_0, b_1, \ldots, b_{n-1} from $D$, there exists a unique index $k$ (0 \leq k < l) such that b_j = a_{(k + j) \bmod l} for all $j$. Construct such a sequence.

Constraints

The integers $n$ and $b$ satisfy: 1 \leq n \leq 1000, 1 \leq b \leq 10, and b^n \leq 10^7.