sub mul2 {
	my ( $str, $have_overflow ) = @_;
	join '', reverse map {
		my $c = $have_overflow ? 1 : 0;
		$c += $_ * 2 if length;
		$have_overflow = ( $c >= 10 );
		# return a zero char only if not at top of string
		( $c % 10 ) or ( length() ? 0 : '' );
	} reverse '', split //, $str;
}