We analyze the evolution of the superconducting gap structure in strongly hole doped Ba1−xKxFe2As2 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 Γ-centered hole pockets (a ++ state on hole pockets). In a pure KFe2As2 (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 φ, which gradually involves from φ = π (the +− state) to φ = 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.