Order of an entire $f $ is $\limsup_{r \rightarrow + \infty} \frac{\log \log M(r)}{\log r}$

Question

An entire function is of finite order $\rho$ if $$\rho = \inf \{\lambda \geq 0 \ | \ \exists A, B > 0 \ s.t. \ |f(z)|\leq Ae^{B|z|^{\lambda}} \forall z \in \mathbb{C} \}$$

Write $M(r) = \sup_{|z|=r}|f(z)|$. Then we have $$\rho = \limsup_{r \rightarrow + \infty} \frac{\log \log M(r)}{\log r}$$

Any hint ?