How to show that $ \mathcal{C}^{\infty} (\mathcal{M}, \mathbb{R}) $ is a nuclear space ?.

Question

Let $ \mathcal{M} $ be a compact differential manifold.

Let $ A = \mathcal{C}^{\infty} (\mathcal{M}, \mathbb{R}) $ be the space of smooth functions over $ \mathcal{M} $.

How to show that $ A $ is a nuclear space ?.

Thanks in advance for your help.