  We investigate the development of the directed, $v_1$, and elliptic flow,
$v_2$, in heavy ion collisions in mid-central Au+Au reactions at
$E_\mathrm{lab}=1.23 A$ GeV. We demonstrate that the elliptic flow of hot and
dense matter is initially positive ($v_2>0$) due to the early pressure
gradient. This positive $v_2$ transfers its momentum to the spectators, which
leads to the creation of the directed flow $v_1$. In turn, the spectator
shadowing of the in-plane expansion leads to a preferred decoupling of hadrons
in the out-of-plane direction and results in a negative $v_2$ for the
observable final state hadrons. We propose a measurement of $v_1-v_2$ flow
correlations and of the elliptic flow of dileptons as methods to pin down this
evolution pattern. The elliptic flow of the dileptons allows then to determine
the early-state EoS more precisely, because it avoids the strong modifications
of the momentum distribution due to shadowing seen in the protons. This opens
the unique opportunity for the HADES and CBM collaborations to measure the
Equation-of-State directly at 2-3 times nuclear saturation density.
