Where were, historicaly, Avars in 1087?

It is known that they invaded Central Europe beggining in 552AD. I've read some books that mention their realm in Northern Hungary from 558AD to 803AD. Charlemagne's attacks, in 791AD and 796AD, eventually destroyed this realm. Nothing else is mentioned and I could not find any note about a possible migration to other parts of Europe. Presumably they left the Frankish borders and moved east.

Is CA correct presenting them in Moldavia in 1087?

Any explanation will be gratefully apreciated...