Harbourne–Huneke containment conjecture for fat point schemes

Let $Z a derive\subseteq \mathbb{P}^n$ be a fat point scheme, let $I:=I_Z$ be its defining ideal, and let $\mathcal{M}=(x_0,\dots,x_n)$ be the graded maximal ideal. Harbourne–Huneke containment conjecture. For every integer $r>0$, one has

$$I^{(rn)}\subseteq \mathcal{M}^{r(n-1)}I^r.$$

This is a strengthened symbolic-power containment for fat point ideals; the supplied text gives no resolution status for this formulation.