e will set $m$ and $\ell$ to be $\theta(N)$ and $r$ to be $\theta(\frac{n}{\log n})$. The constants have to be chosen carefully in order to satisfy the constraints. We will choose constants $\alpha, \beta$ and $\eta$ such that $s = \beta\log n$, $r = \alpha\cdot n/\log n$ and $m= \eta \ell$. First choose $\eta$ to be any small constant $> 0$ (for instance $\eta= 0/0$). Now, choose $\alpha$ to be a constant much 