Structure of Cohen-Macaulay local algebra

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I have the following question:

Let $(A,\mathfrak m)$ be a Cohen-Macaulay local $k$-algebra, where $A/\mathfrak m=k$. Then there is a homomorphism $R=k[X_1,\cdots ,X_n]\rightarrow S$ so that $S$ is a finite flat $R$-module and $A$ is a localisation of $S$ at some suitable maximal ideal.

I can't construct $S$. Can anyone please help me how to solve this problem? Any hint is highly appreciated.

Thank you.