Auto Filling from a Column to Rows, with Changes in Column Data

Hello Everyone!

Appreciate your help here. I have export data where in Column A is the Category, then in Column B is Item ID#, per category. Column A stays empty until the next category. What I want to do is add a dummy column that pastes the proper category into the row it belongs in, while linking to the the proper category group in column A. There is an uneven number of rows per category. This goes on for several thousand categories. Its a little hard to explain in text (because in a way its not "column data" as the title suggests, but row to row data) - a visual makes the problem clear:

This is how the export comes out:
Excel Category Help 1 - Copy.PNG

This is how it should look. In this case I just did it manually, but ideally the solution to filling down column C is formulaic (that's where you guys come in )
Excel Category Help 2 - Copy.PNG

Attached is the sample worksheet.

Thank you everyone for the help

Please try at C2

=IF(B2="","",LOOKUP("zz",A$2:A2))