Perl 'Expert' Quiz-of-the-Week #14

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I thought I wasn't going to get around to doing an Expert quiz, but
I've got a little extra time before I have to leave for the airport,
and a nice short question to ask.

Manufacture a function, 'repeated_substring'.  The argument to the
function is a string.  The function should return the longest
substring of the argument that appears at least twice.  For example,
given "123 1234", the function should return "123".

If there is more than one repeated substring of maximum length, the
function may return any of the substrings.  If there is no repeated
substring, the function should return either undef or an empty string.

The repetitions may *not* overlap.  For example, "ana" is *not*
a repeated substring of "banana".  The longest repeated substrings in
"banana" are "an" and "na".

The function should be efficient, even for very large input strings.