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Is there a way to combine several Beamer presentations into one big presentation?

E.G.: If I have two files a.tex and b.tex which are both presentations, can I compile them into one big presentation?

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An example with docmute:

a.tex

\documentclass{beamer}
\usetheme{Berlin}
\begin{document}
\begin{frame}{test A}
This is A 
\end{frame}
\end{document}

b.tex

\documentclass{beamer}
\usetheme{Madrid}
\begin{document}
\begin{frame}{test B}
This is B
\end{frame}
\end{document}

bigpresentation.tex

\documentclass{beamer}
\title{Big presentation}
\usetheme{Berkeley}
\usepackage{docmute}
\begin{document}
\input{a}
\input{b}
\end{document}

MWE

An similar alternative is the standalone package.

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