Given A = {1, 2, ..., n}, we are going to pick a subset B of size k from A. Please compute the number of ways such that: (a) any two elements in B are not neighboring, i.e., x, y B, |x y| > 1; (b) any two of the selected k elements have distance larger than a, i.e., x, y B, |x y| > a; (c) any two elements in B are not neighboring and 2 / B (assume n > 2).