Show that a derivation mapping k-forms to (k+1)-forms is zero.

Question

This is question 7.4-6 in "Manifolds, Tensor Analysis and Applications", by Marsden, Ratiu and Abraham.

It says: show that a derivation mapping $\Omega^k(M)$ to $\Omega^{k+1}(M)$ for all $k$, is zero.

Here, $M$ is a differential manifold, and $\Omega^k(M)$ denotes the algebra of $k$-forms over M. Also, a derivation is an operator $D$ on $\Omega(M)$ satisfying:

1. If $\omega$ is a $k$-form, then $D(\omega)$is a $(k+r)$-form, for a fixed integer $r$.
2. $D$ is $\mathbb{R}$-linear.
3. $D(\omega \wedge \eta)=D(\omega)\wedge\eta + \omega\wedge D(\eta)$

If $m$ is the dimension of $M$, it is clear that $D$ must send all $m$-forms to zero, for $\Omega^{m+1}(M)=0$. But I don't see how to use this, and otherwise I am at a complete loss regarding properties of such a derivation that are useful to prove the exercise.

Any tip or solution will be highly welcome. Thanks!