Number of paths P19587


Statement
 

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You are located on the point (0, 0) of an infinite integer grid, and you need to go to (x, y). You have two follow two conditions when moving:

  • At every step, you can only go to any of the eight points horizontally, vertically or diagonally adjacent to the point where you currently are.
  • Every movement must strictly reduce the geometric distance to (x, y).

In how many ways can you reach (x, y)?

Input

Input consists of several cases with two integers x and y, each between −2000 and 2000. A case with x = y = 0 ends the input.

Output

For every case, print the number of ways to go from (0, 0) to (x, y). Since this number can be huge, compute it modulo 108 + 9.

Public test cases
  • Input

    0 1
    -1 -1
    0 -2
    -5 3
    2000 2000
    0 0
    

    Output

    1
    3
    7
    9132
    6647843
    
  • Information
    Author
    Salvador Roura
    Language
    English
    Official solutions
    C++
    User solutions
    C++
    Event
    Onzè Concurs de Programació de la UPC - Semifinal
    Date
    2013-06-19