Bounding $c_1c_2...c_k$ if $c_1+c_2+...+c_k<=n$ and $c_i\geq 0$.

Question

As the question asks, given $k\leq n$, and $c_i\geq 0$, is there a way to know the upper bound of $c_1c_2...c_k$ knowing that $c_1+c_2+...+c_k<=n$. I was thinking about the AM-GM inequality but it bounds $c_1c_2...c_k$ from below instead of up. Any help?