Finitely presented module with localization in free module

Question

Let $R$ a commutative ring with unit. Let $M$ a finitely presented $R$-module and let $\mathfrak{p}$ a prime in $R$. Suppose that $M_{\mathfrak{p}}$ is a free module. Prove that there is $a\in R- \mathfrak{p}$ such that $M_a$ is a free module.

Any solution please? I have no ideas...