in latex, how to insert footnote on the first use of \acrshort command?

Question

the footnote inserted for each \acrshort{gcd} but what expected is to insert the footnote on the first use of the command. like the \gls{gcd} command. when the \gls{gcd} command is used, the footnote only inserted on the first use of the command.

here is the minimal not working example:

\documentclass{article}
\usepackage[acronym]{glossaries}

\makeglossaries

\newacronym{gcd}{GCD}{Greatest Common Divisor}

\defglsentryfmt[acronym]{%
  \glsgenentryfmt \ifglsused{\glslabel}{}{\footnote{\glsentrydesc{\glslabel}}}
}

\begin{document}

\acrfull{gcd}\\
\acrshort{gcd} \\
\acrshort{gcd} \\
%\gls{gcd} \\
%\gls{gcd} \\

\printglossary[type=\acronymtype]
\printglossary
\end{document}