Jeremy Kun has an amusing and startling trick: pick any polynomial $p(x)=c_{0}+c_{1}x+\cdots+c_{n}x^{n}$ where the $c_{i}$ are non-negative integers and the degree, $n$, is any positive integer you like. Kun will then ask you one at a time for the value of $p(x)$ at certain points. That is, he will ask for $p(x_{1}), p(x_{2}), \ldots , p(x_{k})$ for $x_{i}$ of his choosing. What is the minimum number of points he will have to ask you about to discover the polynomial?