sub _file_containing {
    my($self, $id) = @_;

    opendir(my $dir, $self->{update_dir}) or return;
    my @files = sort { $a <=> $b } grep { /^\d+$/ && $_ <= $id } readdir $dir;
    return undef if !@files;
    return "$self->{update_dir}/$files[-1]";
}