Prove that $\displaystyle \lim\sup x_n=\infty\iff \forall M>0,\forall n\in\mathbb N,\exists k_0\ge n$ so that $\displaystyle x_k>M.$

I think is an easy problem, but I'm confused, the statement establishes that $\displaystyle x_k$ is bounded below, but not above.

How to prove this?