Packing of the k-power of Hamilton cycles

The k-power of a Hamilton cycle is obtained from it by adding edges between all two vertices whose distance in it is at most k. For sufficiently large n, we determine the maximum number of edges of an n-vertex graph without containing the k-power of a Hamilton cycle, and identify all n-vertex graphs with at most n−2k+ℓ edges which do not pack with the k-power of a Hamilton cycle.