Geometry Class

It's time for the coordinate geometry class. We are given a 2-D grid on which the line x=y and y=0 are drawn. For simplicity assume only the first quadrant is present. You are given q queries to answer. For each query, a line x=a is drawn i.e. a right angled triangle is formed for each query of varying size. Consider all the lattice points on the boundary and inside the triangle formed. (A lattic