VMO 2016 Problem 4

Let $m$ and $n$ be positive integers. A people planted two kind of different trees on a plot tabular grid size $m \times n$ (each square plant one tree.) A plant called inpressive if two conditions following conditions are met simultaneously: i) The number of trees in each of kind is equal; ii) In each row the number of tree of each kind is diffrenent not less than a half of number of cells on that row and In each colum the number of tree of each kind is diffrenent not less than a half of number of cells on that colum.

a) Find an inpressive plant when $m=n=2016$ ; b) Prove that if there at least a inpressive plant then $4|m$ and $4|n$ .