Bolek and Lolek are playing a game known under a familiar name of Pooh-Eeyore-sticks. To play Pooh-Eeyore-sticks only some poohsticks and just as indefinite number of eeyoresticks are necessary. All the sticks, both poohsticks and eeyoresticks, form together the game pool. It is also necessery to choose an arbitrary (positive) integer, traditionally called the PE-bound.
Bolek moves first and can thus remove a certain positive number of poohsticks or eeyoresticks from the game pool. He can also remove both poohsticks and eeyoresticks at once, provided that he picks the same positive number of poohsticks and eeyoresticks. Obviously, he may not pick more poohsticks nor eeyoresticks than there are in the pool. Moreover, neither the number of poohsticks nor eeyoresticks taken away may be greater than the PE-bound.
Subsequent moves are made in turns according to the same rules. The player who first empties the game pool is the winner. Help Bolek prevail against Lolek!

Task

Your task is to write a module that will play as Bolek after being compiled with another playing programme. You will be given a simplified playing programme, so that you will able to test your solution. Your module should contain the following two procedures (functions):

• procedure poczatek (p, e, peb : LongInt) or
  void poczatek (int p, int e, int peb)
  This procedure (function), whose name means beginning in Polish, will be called only once, at the beginning of a game. You may use it to initialize variables or data structures used during the game. Parameters p, e and peb are the numbers of poohsticks and eeyoresticks in the game pool and the PE-bound respectively. The numbers of poohsticks and eeyoresticks in the pool shall be positive and shall not exceed 10^7. PE-bound shall also be positive and shall not exceed 10^6.
  
  
• procedure ruch_bolka (p, e : LongInt; var bm, bp : LongInt) or
  void ruch_bolka (int m, int p, int *bp, int *be)
  This procedure (function) should determine next move of Bolek, as its name in Polish means exactly Bolek's move. The parameters passed, p and e, are the numbers of poohsticks and eeyoresticks respectively left in the game pool after last Lolek's move. The values of the parameters passed to the procedure (function) ruch_bolka in its first call are the same as the values passed to the procedure (function) poczatek. Before termination of the procedure call the values of variables bp, be (*bp i *be in C/C++) should be the numbers of poohsticks and eeyoresticks removed from the pool by Bolek.

Files (Pascal)

In the directory mis_pas you will find the following files:

• mis.pas - a skeleton of the playing module, containing empty procedures poczatek i ruch_bolka. You should fill the code of these procedures.
  
  
• graj.pas - a simplified game-generating programme. Moves of Lolek are made according to a very straightforward strategy, while moves of Bolek are determined by calling the procedures of the playing module mis.pas. You may use this programme to test your playing module.

Files (C / C++)

In the directory mis_c / mis_cpp you will find the following files:

• mis.h - a file containing headers of the functions poczatek and ruch_bolka.
  
  
• mis.c / mis.cpp - a skeleton of the playing module, containing empty definitions of the functions declared in the header file mis.h. You should fill the code of these functions.
  
  
• graj.c / graj.cpp - a simplified game-generating programme. Moves of Lolek are made according to a very straightforward strategy, while moves of Bolek are determined by calling the procedures of the playing module mis.c / mis.cpp.
  You may use this programme to test your playing module.
  

Solution

As a result of your work you should present only one file: either mis.c, or mis.cpp or mis.pas, no more.

Example

This is a sample course of the game:

Call	Description
poczatek(7, 2, 3);	there are 7 Poohsticks, 2 Eeyoresticks, and PE-bound=3
ruch_bolka (7, 2, bp, be); or ruch_bolka (7, 2, &bp, &be);	first move Bolek removes 1 poohstick and 1 eeyorestick from the pool; 6 poohsticks and 1 eeyorestick remain
ruch_bolka (3, 1, bp, be); or ruch_bolka (3, 1, &bp, &be);	Lolek removed 3 poohsticks from the pool; 3 poohsticks and 1 eeyorestick remain Bolek picks 1 poohstick; 2 poohsticks and 1 eeyorestick remain
ruch_bolka (1, 0, bp, be); or ruch_bolka (1, 0, &bp, &be);	Lolek picks 1 poohstick and 1 eeyorestick; 1 poohstick and no eeyorestick remain Bolek removes the final poohstick from the pool and thus wins