  We analyze the evolution of the superconducting gap structure in strongly
hole doped Ba_{1-x}K_xFe_2As_2 between x=1 and x ~ 0.4 (optimal doping). In the
latter case, the pairing state is most likely s+-, with different gap signs on
hole and electron pockets, but with the same signs of the gap on the two
Gamma-centered hole pockets (a ++ state on hole pockets). In a pure KFe_2As_2
(x=1), which has only hole pockets, laser ARPES data suggested another s+-
state, in which the gap changes sign between hole pockets (a +- state). We
analyze how ++ gap transforms into a +- gap as x -> 1. We found that this
transformation occurs via an intermediate s+is, state in which the gaps on the
two hole pockets differ in phase by `phi', which gradually involves from `phi'
= pi (the +- state) to phi =0 (the ++ state). This state breaks time-reversal
symmetry and has huge potential for applications. We compute the dispersion of
collective excitations and show that two different Leggett-type phase modes
soften at the two end points of TRSB state.
