CZ-SK-MO 2005 Problem 1

Consider all arithmetical sequences of real numbers $(x_i)^{\infty}=1$ and $(y_i)^{\infty} =1$ with the common first term, such that for some $k > 1, x_{k-1}y_{k-1} = 42, x_ky_k = 30$ , and $x_{k+1}y_{k+1} = 16$ . Find all such pairs of sequences with the maximum possible $k$ .