Fireworks spread widely (4)

I believe the answer is:

rife

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

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for rife that I've seen before include "Very common or frequently occurring" , "Abounding" , "is everywhere" , "Overabundant" , "raging" .)

I've seen this clue in The Independent.

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