Data List to change in respect to cell value

Hi
I have added the Data Validation - List in one of the cell.
Say it have options A,B,C,D. This is in Cell A1
Now when i select Cell A1 B from the drag drop list, then in Cell B1 it should have a pre defined another list in drag drop . And when i select C it should have another list in the same cell.
Is it possible?

Faisal