When did Tibeto-Burman speakers reach peninsular Southeast Asia?

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Speakers of Tibeto-Burman languages penetrated into peninsular Southeast Asia during the middle of the 1st millennium of the Common Era.1

Prior to their arrival, the region was already inhabited by speakers of Austronesian and Mon-Khmer languages. The Tai peoples also began migrating southward from the north around the same time as the Tibeto-Burman speakers.1