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Bit curious on that so I asked Bing.
Tea originated in China around 2750 BC where it was originally used as medicine. Then from around 202 BC, tea started to be used as a drink in China and different varieties were also discovered. Just 200 years later it was becoming increasingly popular in China. The tea plant is native to East Asia which probably originated in the borderlands of southwestern China and northern Myanmar.

Then I asked about India.
Tea was introduced to India by the British in 1836.

So if Bing's ChatGPT wasn't hallucinating, it went from east to west and then east to south asia.