Let $\pi: X \to \mathbf{P}^2$ be the blow-up of the projective plane at one point. Write $H$ for a hyperplane divisor of $\mathbf{P}^2$. The pullback $\pi^* H$ is big and nef, so it can be written in the form $\pi^* H = A + M$ where $A$ is ample and $M$ is effective with small coefficients.
Does anyone know an explicit description of such an ample + effective decomposition for this particular divisor $\pi^* H$?