This paper presents experiments on morphological inflection using data from the SIGMORPHON-UniMorph 2022 Shared Task 0: Generalization and Typologically Diverse Morphological Inflection. We present a transformer inflection system, which enriches the standard transformer architecture with reverse positional encoding and type embeddings. We further apply data hallucination and lemma copying to augment training data. We train models using a two-stage procedure: (1) We first train on the augmented training data using standard backpropagation and teacher forcing. (2) We then continue training with a variant of the scheduled sampling algorithm dubbed student forcing. Our system delivers competitive performance under the small and large data conditions on the shared task datasets.