Script to copy select folders/files based on an external list in a text file

I have a directory on a windows server that contains over 100,000 documents and I would like to copy some of these to a different drive but I need to preserve the folder structure as well.  I have a list of the folder/file names in a text file and would like a script to automate this process.  How would I do this?

For example, the directory has folders/files similar to this:

C:\Files\AAA\File1.doc
C:\Files\AAA\File2.doc
C:\Files\AAA\File3.doc
C:\Files\BBB\File1.doc
C:\Files\BBB\File2.doc
C:\Files\BBB\File3.doc
C:\Files\CCC\File1.doc
...


My text file might contain something like this:

C:\Files\AAA\File2.doc
C:\Files\BBB\File1.doc
C:\Files\CCC\File3.doc

So I would like my script to loop through the list in the text file and only copy those files while preserving the folder structure.  

So the new directory would be:

D:\Files\AAA\File2.doc
D:\Files\BBB\File1.doc
D:\Files\CCC\File3.doc



Thanks