NL-NWO 1963 Problem 3

Twenty numbers $a_1,a_2,..,a_{20}$ satisfy: $$a_k \ge 7k \,\,\,\, for \,\,\,\, k = 1,2,..., 20$$ $$a_1+a_2+...+a_{20}=1518$$ Prove that among the numbers $k = 1,2,... ,20$ there are no more than seventeen, for which $a_k \ge 20k -2k^2$ .