Copy Paste and Loop till last column with data

Hi there. Please help.
I have data spanning across over 10,000 rows and need to copy and paste months (Jan-Dec in column A of this data. I therefore need a macro that will loop through the spreadsheet until there's no more data in column B.

It looks like this:

Month Cost Centre
Jan 30002000
Feb 30002000
Mar 30002000
Apr 30002000
May 30002000
Jun 30002000
Jul 30002000
Aug 30002000
Sep 30002000
Oct 30002000
Nov 30002000
Dec 30002000
30002001
30002001
30002001
30002001
30002001
30002001
30002001
30002001
30002001
30002001
30002001
30002001
30002002
30002002
Please help. Many thanks.

hi, eirumba, please check attachment, run code "FillMonths"