Explain How Buddhism Spread in India and China

Explain how Buddhism spread in India and China.B.C.E. ,the emperor Ashoka made Buddhism the state religion of India.Ashoka's role in spreading Buddhism foreshadowed Constantine's labors on behalf of Christianity;but Ashoka went even further.He initiated official policies of non-violence,promoted vegetarianism,and defended egalitarianism.He built monuments and shrines honoring the Buddha throughout India and he sent Buddhist missionaries as far west as Greece and southeast into Ceylon (present-day Sri Lanka).
Despite Ashoka's efforts,Buddhism never gained widespread popularity in India.The strength of the established Hindu tradition there (like that of Judaism in Judea)and the resistance of the Brahmin caste to Buddhist egalitarianism ultimately hindered the success of the new faith.Buddhist communities nevertheless continued to 
flourish in India until the
 Islamic invasion of north
ern India in the twelfth and thirteenth centuries,during which
 time Buddhism became all
 but extinct.Buddhism did,however,continue to thrive
 in lands far from its place 
of birth.In China,Mahayana Buddhism gained an overwhelming following and influence.From China,the new religion spread also to Korea,Japan,and Vietnam,where its impact was similarly great.Buddhism's tolerance for other religions enhanced its popularity and universal appeal.