A restriction of a distribution

Question

Let $T\in\mathcal{D}'\left(\left(-1,-1\right)\right)$ be a distribution on $\left(-1,1\right)\subset\mathbb{R}$ and let $G$ be the restriction of $T$ to $\left(-\frac{1}{2},\frac{1}{2}\right).$ Prove that there exist continuous functions $f_{0},\ldots,f_{m}\in C\left(\left[-\frac{1}{2},\frac{1}{2}\right]\right)$ such that $$ G=\sum_{k=0}^{m}\frac{d^{k}}{dx^{k}}\left(f_{k}\right), $$ as distributions on $\left(-\frac{1}{2},\frac{1}{2}\right)$.