In a TV game show, Jack and Jill are placed in separate rooms where each is given a number between 1 and N.

Each room has a red button that lights a red light in the other room, and a green button that lights a green light in the other room.

Jack goes first. He presses either the green or the red button in his room which lights the corresponding light in Jill's room. Then it is Jill's turn to press one of her buttons, and so on.

Jack and Jill have a common objective: to determine whether or not they have been given the same number. At any time, either Jack or Jill may call out same! or different!, which terminates the game.

Your task is to implement two program components, jack and jill that together will play the game. The master of ceremonies is implemented by the program component gameshow which is supplied by IOI.

Jack must implement two procedures: jackstart(N,K) and jacksturn(C). Jill must implement two procedures: jillstart(N,L) and jillsturn(C). jackstart(N,K) will be called by the grader exactly once at the start of the game, specifying N as described above and Jack's secret number K, which will be between 1 and N. jillstart(N,L) will similarly be called at the start of the game, indicating N and Jill's secret number L. Then jacksturn(C) and jillsturn(C) will be called alternately, starting with jacksturn

The parameter C is an integer indicating the color of button pressed by the other player: C=0 indicates "none" and is used only for the first call to jacksturn(C). C=1 indicates "green" while C=2 indicates "red."

jacksturn and jillsturn should return:

• 1 to press the green button
• 2 to press the red button
• 3 if Jack or Jill has determined that K and L are equal
• 4 if Jack or Jill has determined K and L are not equal

Note: Jack and Jill must communicate only through the specified interface. Shared variables, file access and network access are prohibited. In C or C++, you may declare persistent variables to be static to retain information for Jack or Jill, while preventing them from being shared. In Pascal, you may declare persistent variables in the implementation part of your solution files.

Implement any correct strategy for N=10. The implementation files described below contain a solution to this subtask.

Implement any correct strategy for N=10 that yields the correct answer with no more than 10 calls to jacksturn and jillsturn, in total.

Implement any correct strategy for N=10 that yields the correct answer with no more than 5 calls to jacksturn and jillsturn, in total.

Implement any correct strategy for N≤1,000,000,000 that runs within the time limit of 10 seconds.

Implementation Details

• Use the RunC programming and test environment
• To be implemented by contestant:
• jack.c or jack.cpp or jack.pas
• jill.c or jill.cpp or jill.pas
• Contestant interface:
• jack.h or jack.pas
• jill.h or jill.pas