amazing boundedness problem from maximal function

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Let $n\geq 2$. For any $M>1$, prove that there exists a constant $C_M>1$ such that for any ball $B$ in $\mathbb{R}^n$, if we denote $MB$ as the concentric ball of $B$ with $M$ times radius of $B$, then

$$ \int_{MB}\frac{dx}{|x|}\leq C_M\int_B\frac{dx}{|x|} $$

How to prove?