KöMaL 2006 A408

The positive reals $a_1,a_2,\ldots,a_n$ and $b_1 \le b_2 \le^{...} \le b_n$ satisfy $a_1$+$a_2 +^{...}$+$a_k \le b_1$+$b_2 +^{...}$+$b_k$ for all 1$\le k \le n$. Prove that $\frac1{a_1}+\frac1{a_2}+\cdots+\frac1{a_n} \ge \frac1{b_1}+\frac1{b_2}+\cdots+\frac1{b_n}.$