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opendir DIR, $logs or die "Cannot open dir $logs: $!\n";
my @files = grep /^access_log\.\d+\.gz$/, readdir DIR;
...
    or die "Cannot open tar: $!\n";
print TAR $_, "\n" for @files;
close TAR or die "error closing TAR: $!\n";

print TAR "$logs/$_\n" for @files;