Joining data from one model into another based on a specific field and store this data in an array

I am creating a movie booking application and I am looking to store an array of IDs into the Movies document in a shows array from the Shows document, although only if the title matches in both.

For example if I have 3 different show times for Movie-A in the Shows model and want to store all these IDs for Movie-A in the shows array on the Movie model , only if the title in the Movies document is also Movie-A.

Here is some example data -

The array in the Movies document is currently empty