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)~