Greek --> Indian influence: How Early?

Factual Questions
1

I know there was influence on Indian culture from Greece, but how far back does it go?

Is there any evidence of influence going the other direction? Or common influences on both?

-FrL-

2

The very latest date would be when Alexander invaded India about 330 BC

Doing a quick check for a roughly accurate date I found this: Opium Timeline

Serendipity.