solve k =
  if k == 0
    then 0
    else extract . dropWhile (notSameOddity k') . dropWhile (notIncludes k') . enhance $ [0..]
  where
    k' = abs k
    sums = scanl (+) 0 [1..]
    enhance = zip3 (cycle [0, 1, 1, 0]) sums
    first  (x, _, _) = x
    second (_, x, _) = x
    third  (_, _, x) = x
    notIncludes k = (< k) . second
    notSameOddity k = (/= k `rem` 2) . first
    extract = third . head

assertEq x y =
    if x == y
    then return ()
    else error $ "Assertion violated: first argument is " ++ show x ++ " but second argument is " ++ show y

assertEq' = uncurry assertEq

main = do
    assertEq' (solve 2,  3)
    assertEq' (solve 12, 7)
    putStrLn "Tests passed"