Drawing conclusion on function differentiability based on the fourier coefficient bound

Question

Assume that $f \in L^{1}([-\pi, \pi])$, and $\sum_{n \in \mathbb{Z}} |n|^{k} |\tilde{f}(n)| < \infty$ for some $k \geq 0$. prove that the function $\tilde{f}: \mathbb{R} \rightarrow \mathbb{C}$ defined by $$ \tilde{f}(x)= \sum_{n \in \mathbb{Z}} \tilde{f}(n)e^{inx} $$ is well defined, $\tilde{f} \in C^{k}([-\pi, \pi])$ and $f(x)= \tilde{f}(x)$ for lebesgue almost every $x \in \mathbb{R}$ can someone provide me some small hint, I am familiar with only converse direction type of question, where we show decay on fourier coefficient based on differentiability of function, this one i am not sure how to start. thank you.