The beginning of the age of pirates

Gol D. Roger, the pirate king, conquered everything this world has to offer. Before being executed, he hid his treasure, the "One Piece" on an island on the Grand Line. The Grand line is a group of $$$N$$$ islands in the sea numerated from $$$1$$$ to $$$N-1$$$. Due to its weather conditions, the Grand line cannot be traversed as any typical sea; any travel on the Grand line has to start on the Red line, which is represented by the number $$$0$$$, and follow the sea routes. There are $$$N-1$$$ unidirectional sea routes that connect two islands. From each island, it is also possible to go back directly to the Red Line. It is known that every island can be reached from the Red line following sea Routes.

Roger will hide the $$$m$$$ maps to his treasure on islands throughout the Grand line, and each map will have to be recovered in order and then brought back to the Red line before you can go to the next one. To make sure the journey to the One Piece is as fun as it should be, Roger wants to know $$$\sum b_i$$$ where $$$b_i$$$ represents how many times a pirate crew that started on the Red line, and has followed the shortest path that follows the conditions (Get the maps in order, always return to the Red line after recovering a map), has passed through the island $$$b_i$$$ before collecting map $$$i$$$.