Why did Buddhism, originating in India, spread more widely along the Spice Route?

Why did Buddhism, originating in India, spread more widely along the Spice Route? Was there something similar in the spread of Christianity?

The positions of Buddhism in India were undermined after the overthrow of the power of the Kushan Buddhist kings. Their winners – the Gupta kings – preferred the national religion of Hinduism to “international” Buddhism. Similarly, Christianity was ousted from its historical homeland – Palestine, Egypt and Syria under the pressure of the new local religion – Islam.

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