У самого (+ masculine noun in genitive case)... У самой (+ feminine noun in genitive case)...
I guess that the initial form of these pronouns may be either "сам"/"сама" or "самый"/"самая". Unfortunately, it's written text and the book does not provide any accent marks. So how would you determine if it's a form of сам or самый?
The initial form (and the stress) depends on the meaning:
са́мого, са́мой (from са́мый) usually come before an adjective to form the superlative: са́мого лу́чшего, са́мой краси́вой.
самого́, само́й (from сам) mean 'himself', 'herself' and usually come after a personal pronoun: его́ самого́, ей само́й or before a noun: самого́ президе́нта, само́й ма́тери Тере́зы.
See which meaning better fits the context.
