In a gulping manner; with audible swallows or in large amounts.
From 'gulping' (present participle of gulp) plus the adverbial suffix '-ly,' creating an adverb that describes how an action is performed.
The suffix '-ly' transforms almost any adjective or gerund into an adverb in English, which is why 'gulpingly' is understood immediately even though it's rarely written—we can create thousands of adverbs following this simple pattern.
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