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It came from the trade routes , my reason being is because along the trade routes many things were traded , not only food salt or gold but religion was too.

It impacted Japan so much that most people Today would say that Japan created it . 

Japan actually use to be confused , meaning that they had no religion.

I really hope that this helps you out a lot. 
Buddhism reached Japan through trade routes. See besides trade goods religion and languages were also traded in a way.Hope this helps!  :)