Maximal Function of $|x|^{-\alpha}$ in $\mathbb{R}^d$

Question

Is it true that if $f_{\alpha}(x)=|x|^{-\alpha}$ with $f_{\alpha} \in L^1_{loc}(\mathbb{R}^d)$, that means $0<\alpha<d$, there exists a constant $C_{\alpha,d}$ such that \begin{align*} \mathcal{M}f_{\alpha}(x)=\sup_{r>0}\dfrac{1}{m(B_r(x))} \int_{B_r(x)} |y|^{-\alpha} dy=C_{\alpha,d}f(x) \end{align*} ?
If so, when is $C_{\alpha,d}>1$? I am trying to write the integral as \begin{align*} \int_0^{\infty} m\left( \{y \in B_r(x) : |y|^{-\alpha} >t\right) dt \end{align*} but did not lead to any result. Thank you.