B"The map of Bertown can be represented as a set of n intersections, numbered from 1 to n and connected by m one-way roads. It is possible to move along the roads from any intersection to any other intersection. The length of some path from one intersection to another is the number of roads that one has to traverse along the path. The shortest path from one intersection v to another intersection u is the path that starts in v , ends in u and has the minimum length among all such paths. Polycarp lives near the intersection s and works in a building near the intersection t . Every day he gets from s to t by car. Today he has chosen the following path to his workplace: p_1 , p_2 , ..., p_k , where p_1 = s , p_k = t , and all other elements of this sequence are the intermediate intersections, listed in the order Polycarp arrived at them. Polycarp never arrived at the same intersection twice, so all elements of this sequence are pairwise distinct. Note that you know Polycarp's path beforehand (it is fixed), and it is not necessarily one of the shortest paths from s to t . Polycarp's car has a complex navigation system installed in it. Let's describe how it works. When Polycarp starts his journey at the intersection s , the system chooses some shortest path from s to t and shows it to Polycarp. Let's denote the next intersection in the chosen path as v . If Polycarp chooses to drive along the road from s to v , then the navigator shows him the same shortest path (obviously, starting from v as soon as he arrives at this intersection). However, if Polycarp chooses to drive to another intersection w instead, the navigator rebuilds the path: as soon as Polycarp arrives at w , the navigation system chooses some shortest path from w to t and shows it to Polycarp. The same process continues until Polycarp "...