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As they usually do, N robots are playing the game of Werewolf, and the robots are numbered with integers from 1 to N. Exactly W of these robots are werewolves, and the remainder are civilians. Though the game of Werewolf involves various aspects, we will focus on a single discussion phase of the game.
Robots accuse other robots of being werewolves and defend other robots by vouching for their innocence.
The werewolves know each other’s identities and:
Civilians may accuse or defend either type of robot. Additional constraints make our task a bit easier:
You will be given all the accusations and defenses between N robots where there are exactly W werewolves. A role assignment identifies each of the robots as either werewolf or civilian. Your goal is to figure out how many role assignments satisfy all the above constraints.
The first line contains three numbers (each separated by one space):
The next M lines give the accusations and defenses. Each of these lines will be one of the following two forms:
Output the number of role assignments that are consistent with the given information. Since this number may be very large, you must output this answer modulo 109 + 7.
2 1 1 D 1 2
If robot 1 is a werewolf, then robot 2 must also be, which is too many werewolves! The only possibility is that robot 2 is the sole werewolf.
2 1 0
With no information, either robot 1 or robot 2 could be a werewolf.
3 2 2 A 1 2 D 1 3
Either robot 1 is a werewolf, which implies robot 2 is a civilian and robot 3 is a werewolf as well, or robot 1 is a civilian (which allows robots 2 and 3 to both be werewolves).