MK-MO 2008 Problem 4

We call an integer $n > 1$ good if, for any natural numbers $1 \le b_1, b_2, \ldots , b_{n-1} \le n - 1$ and any $i \in \{0, 1, \ldots , n - 1\}$ , there is a subset $I$ of $\{1, \ldots , n - 1\}$ such that $\sum_{k\in I} b_k \equiv i \pmod n$ . (The sum over the empty set is zero.) Find all good numbers.