Knights and Knaves - Another Truth and Liar Problem

An island has only two types of people: Knights (who always speak the truth) and Knaves (who always lie).

I met two men who lived there and asked the taller man "Are both of you Knights?".
He replied with a "Yes" or "No", but from his answer, I could not figure out what type of person each man was.
I then asked the shorter man "Is the taller man a Knight?".
He replied with a "Yes" or "No", and after that I knew which type of person each man was.

Were the men Knights or Knaves?

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