RU-ALLRUSSIAN 1980 Problem 11

Let $\mathbf{f}(\mathbf{n})$ be the sum of $\mathbf{n}$ and its digits. For example, $\mathbf{f}(34) = 41$ . Is there an integer such that $\mathbf{f}(\mathbf{n}) = 1980$ ? Show that given any positive integer $\mathbf{m}$ we can find $\mathbf{n}$ such that $\mathbf{f}(\mathbf{n}) = \mathbf{m}$ or $\mathbf{m} + 1$ .