In QAOA why do we need $m \log(m)$ repetitions to get at least $F_{p}(\beta , \gamma) - 1$ with probability of $1 - 1/m$?

Question

In the original QAOA paper from Farhi https://arxiv.org/pdf/1411.4028.pdf, it is stated in chapter 2 last paragraph (page 6) that: when measuring $F_{p}(\beta , \gamma)$ we get an outcome of at least $F_{p}(\beta , \gamma) - 1$ with probability of $1 - 1/m$ with order $m \log(m)$ repetitions.
Where is this proven? Or what is the idea behind that?

Thanks:))