Conflict-free coloring is a kind of vertex coloring of hypergraphs requiring each hyperedge to have a color which appears only on one vertex. More generally, for a positive integer there are -conflict-free colorings (-CF-colorings for short) and -strong-conflict-free colorings (-SCF-colorings for short). Let be the hypergraph of which the vertex-set is and the hyperedge-set is the set of all (non-empty) subsets of consisting of consecutive elements of . Firstly, we study the -SCF-coloring of , give the exact -SCF-coloring chromatic number of for , and present upper and lower bounds of the -SCF-coloring chromatic number of for all . Secondly, we give the exact -CF-coloring chromatic number of for all .