I have problem with prooving those two identities. Any help would be much appriciated!

Show that:

a)

$\displaystyle \begin{Bmatrix} m+n+1\\ m\end{Bmatrix}= \sum_{k=0}^{m} k\begin{Bmatrix}n+k\\k \end{Bmatrix}$

b)

$\displaystyle \sum_{k=0}^{n} \begin{pmatrix}n\\k \end{pmatrix}\begin{Bmatrix}k\\m \end{Bmatrix}= \begin{Bmatrix}n+1\\m+1 \end{Bmatrix}$

Where:

$\displaystyle \begin{Bmatrix}k\\m \end{Bmatrix}$

is a Stirling number of the second kind.