sub mul2 {
	my ( $str, $have_overflow ) = @_;

	my $ret = join '', reverse map {
		my $c = $_ * 2 + ( $have_overflow ? 1 : 0 );
		$have_overflow = ( $c >= 10 );
		( $c % 10 );
	} reverse split //, $str;

	( $have_overflow ? 1 : '' ) . $ret;
}