This is another simple implementation problem. In order to check if a point $(x_i,y_i)$ is on the polynomial, all we have to do is check if $f(x_i)$ is equal to $y_i$. In order to check if a point $(x_i,y_i)$ is within the ending explosion, we need to find the ending point, which is located at $(V,f(V))$, and use the Euclidean distance formula to determine if the distance between $(x_i,y_i)$ and $(V,f(V))$ is less than or equal to $R$. In order to quickly determine values of $f(x)$, we can pre-compute all values of $f(x)$ from $0$ to $V$, but this is not necessary to pass.

However, there are some important corner cases to check. The first is that we should not evaluate $f(x)$ if $x>V$ since the point could not possibly be on the polynomial. Next, we need to make sure that a point that is on the polynomial and within the explosion is not counted twice. Additionally, one should use either floating point numbers or 64-bit integers to compute distances.

Time Complexity: $\mathcal{O}(N+VP)$