We fix two non-zero natural integers $n$ and $m$ as well as two polynomials $Q \in \mathbb{C}[X]$ and $R \in \mathbb{C}[X]$ of degrees $n$ and $m$ respectively. We introduce the polynomial $P = QR$. We set $w = \frac{v}{u}$. Show that:
$$M(S) \leq \|P\|_{\mathbb{D}} \exp\left(\frac{n+m}{2\pi} \int_0^{2\pi} \ln\left(\max\left\{\left|e^{i\theta} - 1\right|, \left|e^{i\theta} - w\right|\right\}\right) d\theta\right)$$