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In this paper, we use large language models to generate personalized stories for language learners, using only the vocabulary they know.The generated texts are specifically written to teach the user new vocabulary by simply reading stories where it appears in context, while at the same time seamlessly reviewing recently learned vocabulary. The generated stories are enjoyable to read and the vocabulary reviewing/learning is optimized by a Spaced Repetition System.The experiments are conducted in three languages: English, Chinese and Polish, evaluating three story generation methods and three strategies for enforcing lexical constraints. The results show that the generated stories are more grammatical, coherent, and provide better examples of word usage than texts generated by the standard constrained beam search approach.