Problem Statement  
A bishop is a chess piece that can move any number of squares in any diagonal direction (see diagram below). The chess board has dimensions xSize * ySize, where the topleft corner of the board has coordinates (0, 0), and the bottomright corner has coordinates (xSize  1, ySize 1). The bishop is initially at coordinates (x, y). Find the total number of squares reachable by this bishop in k or less moves. Note, that initial square is always counted as reachable.  
Definition  
 
Constraints  
  xSize will be between 2 and 50000, inclusive.  
  ySize will be between 2 and 50000, inclusive.  
  x will be between 0 and xSize  1, inclusive.  
  y will be between 0 and ySize  1, inclusive.  
  k will be between 1 and 50000, inclusive.  
Examples  
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