Basically, it is sufficient to simulate just as instructed in the problem statement. One issue is the spacial complexity. If you manage the positions of the items with a two-dimensional array, the spacial complexity becomes \(\mathrm{O}(X^2)\), where \(\mathrm{max}(|x_i|,|y_i|)=X\).

To improve this, it is enough to manage the items with a data structure like std::set. With this improvement, the problem can be solved with both the time and spacial complexity of \(\mathrm{O}(N + M\log M)\).