CMO 1993 Problem 2

Given a natural number $k$ and a real number $a (a>0)$ , find the maximal value of $a^{k_1}+a^{k_2}+\cdots +a^{k_r}$ , where $k_1+k_2+\cdots +k_r=k$ ( $k_i\in \mathbb{N} ,1\le r \le k$ ).