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Jun 9th, 2019
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  1. In the nation of CodeWars, there lives an Elder who has lived for a long time. Some people call him the Grandpatriarch, but most people just refer to him as the Elder.
  2.  
  3. There is a secret to his longetivity: he has a lot of young worshippers, who regularly perform a ritual to ensure that the Elder stays immortal:
  4.  
  5. - The worshippers lines up in a magic rectangle, of dimensions m and n.
  6. - They channel their will to wish for the Elder. In this magic rectangle, any worshipper can donate time equal to the xor of the column and the row (zero-indexed) he's on, in seconds, to the Elder.
  7.  
  8. - However, not every ritual goes perfectly. The donation of time from the worshippers to the Elder will experience a transmission loss l (in seconds). Also, if a specific worshipper cannot channel more than l seconds, the Elder will not be able to receive this worshipper's donation.
  9. - The estimated age of the Elder is so old it's probably bigger than the total number of atoms in the universe. However, the lazy programmers (who made a big news by inventing the Y2K bug and other related things) apparently didn't think thoroughly enough about this, and so their simple date-time system can only record time from 0 to t-1 seconds. If the elder received the total amount of time (in seconds) more than the system can store, it will be wrapped around so that the time would be between the range 0 to t-1.
  10.  
  11. Given m, n, l and t, please find the number of seconds the Elder has received, represented in the poor programmer's date-time system.
  12.  
  13. (Note: t will never be bigger than 2^32 - 1, and in JS, 2^26 - 1.)
  14.  
  15.  
  16. EXAMPLE
  17. m=8, n=5, l=1, t=100
  18.  
  19. Let's draw out the whole magic rectangle:
  20. 0 1 2 3 4 5 6 7
  21. 1 0 3 2 5 4 7 6
  22. 2 3 0 1 6 7 4 5
  23. 3 2 1 0 7 6 5 4
  24. 4 5 6 7 0 1 2 3
  25.  
  26. Applying a transmission loss of 1:
  27. 0 0 1 2 3 4 5 6
  28. 0 0 2 1 4 3 6 5
  29. 1 2 0 0 5 6 3 4
  30. 2 1 0 0 6 5 4 3
  31. 3 4 5 6 0 0 1 2
  32.  
  33. Adding up all the time gives 105 seconds.
  34.  
  35. Because the system can only store time between 0 to 99 seconds, the first 100 seconds of time will be lost, giving the answer of 5.
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