Nested enumerate list ending with a character

Question

I am trying to have a nested enumerate item ending with a special character; in my case ")" character. According to some answers, people were suggesting making something like:

\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage[shortlabels]{enumitem}


\begin{document}
\begin{enumerate}[label=\arabic*)]
    \item first item
    \begin{enumerate}[label*=.\alph*)]
        \item sub item
        \item another sub item
    \end{enumerate}
    \item another item
    \item one more item
\end{enumerate}
\end{document}

However, what I get by using this instruction is

1) first item
    1).a) sub item
    1).b) another sub item
2) another item
3) one more item

but what I want is

1) first item
    1.a) sub item
    1.b) another sub item
2) another item
3) one more item

How can I accomplish this type of numbered list?

Answer 1

inputenc is no longer needed. utf8 is the default since more than four years.

\documentclass[10pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage[shortlabels]{enumitem}


\begin{document}
\begin{enumerate}[label=\arabic*)]
    \item first item
    \begin{enumerate}[label=\arabic{enumi}.\alph*)]
        \item sub item
        \item another sub item
    \end{enumerate}
    \item another item
    \item one more item
\end{enumerate}
\end{document}