  We study the superconducting state in newly discovered high-Tc superconductor
K$_x$Fe$_2$Se$_2$ based on the ten-orbital Hubbard-Holstein model without
hole-pockets. When the Coulomb interaction is large, spin-fluctuation mediated
d-wave state appears due to the nesting between electron-pockets.
Interestingly, the symmetry of the body-centered tetragonal structure in
K$_x$Fe$_2$Se$_2$ requires the existence of nodes in the d-wave gap, although
fully-gapped d-wave state is realized in the case of simple tetragonal
structure. In the presence of moderate electron-phonon interaction due to
Fe-ion optical modes, on the other hand, orbital fluctuations give rise to the
fully-gapped $s_{++}$-wave state without sign reversal. Therefore, both
superconducting states are distinguishable by careful measurements of the gap
structure or the impurity effect on Tc.
