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 