Given $\lim a_n =a$ and $\lim b_n =b$, show $\lim\frac{1}{n}\sum_{k=1}^{n}a_k b_{n+1-k}=ab$

Question

Given $\lim a_n =a$ and $\lim b_n =b$, show $\lim\frac{1}{n}\sum_{k=1}^{n}a_k b_{n+1-k}=ab$

As you can see, two limit are expanding in two different direction. I have no idea about how to do it.