  We studied the pairing instabilities in K$_x$Fe$_{2-y}$Se$_2$ using a two
stage functional renormalization group (FRG) method. Our results suggest the
leading and subleading pairing symmetries are nodeless $d_{x^2-y^2}$ and nodal
extended $s$ respectively. In addition, despite having no Fermi surfaces we
find the buried hole bands make important contributions to the final effective
interaction. From the bandstructure, spin susceptibility and the FRG results we
conclude that the low energy effective interaction in K$_x$Fe$_{2-y}$Se$_2$ is
well described by a $J_1-J_2$ model with dominant nearest-neighbor
antiferromagnetic interaction $J_1$ (at least as far as the superconducting
pairing is concerned). In the end we briefly mention several obvious
experiments to test whether the pairing symmetry is indeed $d_{x^2-y^2}$.
