Actually, the Japanese went to the mainlad as early as 5th century, granted no mass invasions but their contact may even go beyond that. Artefacts from Silla has been found in Japan. Also, Hideyoshi had a huge invason of the Korean peninsula late in the 16th century, yes, it failed miserably, but when these things happen people are left behind.
The reason I just wanted to point at the opposite being a possibility is that there were never, as far as we know, any large scale migration the other way around.
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