Transitive permutation groups with elements of movement m or m − 2

Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If for each subset of the size |ᵍ| is bounded, for g G, we define the movement of g as the |ᵍ| over all subsets of, and the movement of G is defined as the maximum of move (g) over all non-identity elements of g G. In this paper we classify all transitive permutation groups with bounded movement equal to m that are not a 2-group, but in which every non-identity element has movement m or m-2.