On success runs in a sequence of dependent trials with a change point

Let Xii=1n be a sequence of n dependent binary trials such that the first n1 in Xii=1n are of type 1 and follow an exchangeable joint distribution denoted by L1, and the last n2 elements in Xii=1n are of type 2 and follow an exchangeable joint distribution denoted by L2, where n1+n2=n. That is, the trials within the same group are exchangeable dependent, and the trials in different groups are dependent in a general sense. The exact distributions of the number of success runs of length k in Xii=1n are obtained under nonoverlapping and at least schemes.