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\[N_{n,k}\triangleq\left\{{\left.{\left[X_0,X_1,\cdots,X_{k-2},S+\sum_{i=0}^{k-2}X_i\right]}\right|}{[b_0, b_1, \cdots, b_{k-1}]\in N_k^{\prime 0}\cup N_k^{\prime 1},X_i\in X_n^{b_i},0\leq i<k-1,S\in N_n^p,p=\sum_{i=0}^{k-1}b_i}\right\}.\]
