CN-LEAGUE 2014 Problem 4

Let $x_1,x_2,\dots,x_{2014}$ be integers among which no two are congurent modulo $2014$ . Let $y_1,y_2,\dots,y_{2014}$ be integers among which no two are congurent modulo $2014$ . Prove that one can rearrange $y_1,y_2,\dots,y_{2014}$ to $z_1,z_2,\dots,z_{2014}$ , so that among $$x_1+z_1,x_2+z_2,\dots,x_{2014}+z_{2014}$$ no two are congurent modulo $4028$ .