No greek small caps with Libertine (pdflatex)

Question

I'm trying to get libertine small caps to work with greek, with the following MWE:

\documentclass[a4paper,12pt]{report}

\usepackage{geometry}

\usepackage[LGR,T1]{fontenc}
\usepackage[utf8]{inputenx}
%\usepackage[utf8x]{inputenx}
\usepackage[english,greek]{babel}

\usepackage{libertine}
%\usepackage{libertinegc}
\usepackage{libertinust1math}

\begin{document}

\selectlanguage{greek}
\textsc{Τα Πεζοκεφαλαία δεν δουλεύουν.}
\end{document}

but instead it fails and reverts back to the regular font. In their website they seem to have small caps working with greek, but in pdflatex they don't seem to work.