Search for files and retrieve file size recursively

Using below snippet - is there a way to retrieve the size of the file and print in the below line:
   print "$dir/$_\n" if (/\.exe/

Snippet:

$BASEDIR =  "\\\\remote/path/basedirectory/";    #give your required base directory
$temp = $BASEDIR;
#$outfile = "$temp/list";    # give the location of the output file
#open OUT, ">$outfile" or die "Cannot open $outfile";
 
chdir $BASEDIR or die "Cannot cd to $BASEDIR: $!n";
traverse($BASEDIR,(stat('.'))[3]);
 
 
# @FILES now contains a list of file paths.
 
sub traverse {
my ($dir,$nlink) = @_;
my (@filenames,@subdirs);
 
opendir DIR, '.' or die "cannot opendir $dir: $!n";
@filenames = grep { !/^..?$/ && !(-l $_) } readdir DIR;
closedir DIR;
 
for (@filenames) {
next unless stat($_) && -r _;
-d _ && push(@subdirs,$_);
-f _ && -s _ && -T _ && m{..?html?$} && push(@FILES,"$dir/$_");
 if($_ =~/\./)
  {
   print "$dir/$_\n" if (/\.exe/);
   #print OUT "$a"
  }
 
}
 
# has subdirs
if ($nlink != 2) {
for (@subdirs) {
chdir $_ or die "cannot cd to $_: $!n";
traverse("$dir/$_",(stat('.'))[3]);
chdir '..';
}
}
}