How a bright idea comes to you? (2,1,5)

I believe the answer is:

in a flash

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'how' is the definition.
Both the answer and definition are adverbs. Maybe you can see a link between them that I don't see?

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for in a flash that I've seen before include "Where American detected electricity" , "Almost instantly" , "How lightning appears" , "Very quickly" , "Instantly, straightaway" .)

I've seen this clue in The Globe and Mail.

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