MathNet 1968 — Part 01 Question 2

$\{a_i\}$ and $\{b_i\}$ are permutations of $\{1/1, 1/2, \dots, 1/n\}$. $a_1 + b_1 \geq a_2 + b_2 \geq \ldots \geq a_n + b_n$. Prove that for every $m$ ($1 \leq m \leq n$), $a_m + b_m \geq \dfrac{4}{m}$.