How to show that this sum is zero, $\sum^{k}_{j=0}\frac{(-1)^{j}}{j!(k-j)!} $ whenever $k \ge 1$?

Question

Is there a simple way to prove this sum, $$S_{k} =\sum^{k}_{j=0}\frac{(-1)^{j}}{j!(k-j)!}~ ,$$ is zero whenever $k \ge 1$? Whenever $k$ is odd, I know I can pair up the terms and it cancels out, but I'm not sure to do whenever $k$ is even.