Statement

Marco is studying electronics at Politecnico di Milano and his teacher assigned him an experimental project to do at the lab. The project is pretty simple: he has a circuit board with N connection points, and he should connect M components to those points, in the given order from component 0 to M-1. Each component i has a characteristic integral potential difference z_i and two terminals, which have to be connected to two given connection points a_i and b_i. Once a circuit is built, each of the connection points j=0 … N-1 naturally acquires a potential P_j. Furthermore, the i-th component can work correctly only provided that the difference of the potentials of its terminals is exactly z_i: in formulas, if P_a_i - P_b_i = z_i (or equivalently P_b_i - P_a_i = -z_i: the orientation of components matters). The laws of electromagnetism ensure that whenever an assignment of potentials satisfying the potential differences of components exists, such an assignment will naturally arise...