How do I know exact extension of a Word document in Java

How do I know exact extension of a Word document in Java

I have a program which copies a word file (docx/doc) as follows:

InputStream in = new FileInputStream ( src );
OutputStream out = new FileOutputStream ( dst );
byte [] buf = new byte [1024];
int len;
while ( ( len = in.read ( buf ) ) > 0 ) {
out.write ( buf, 0, len );
}
Destination dst is a raw file without any extension (say, 'sample-file'),
which I can't change. The sourcesrc may be a 'doc' or a 'docx' type.
Now, as an output, I need to copy the contents of dst to a Word Document
with proper format as of src(this 'proper format' is important here,
otherwise the document is rendered useless). Since dst doesn't have any
extension, I cannot find the file format by just looking at the name. Is
there a way, I can retrieve the file extension from file contents?
Hopefully, Word document must have some meta-data containing this
information.