{-# OPTIONS_GHC -Wno-unused-top-binds #-}

mex :: (Functor f, Foldable f, Eq b, Num b, Num a) => f b -> a
mex s = if 0 `notElem` s then 0 else 1 + mex (fmap (+ (-1)) s)
-- | Compute nimber sum directly from the definition.  This is very slow.
nimberAdd :: Int -> Int -> Int
nimberAdd = (!!) . (nimberSumTable !!)
nimberSumTable :: [[Int]]
nimberSumTable = fmap add <$> [(i,) <$> [0 ..] | i <- [0 ..]]
  where
    add (a, b) = mex $ [nimberSumTable !! a' !! b | a' <- [0 .. a - 1]] ++ [nimberSumTable !! a !! b' | b' <- [0 .. b - 1]]
-- | Compute nimber product directly from the definition.  This is very slow.
nimberMul :: Int -> Int -> Int
nimberMul = (!!) . (nimberProdTable !!)

nimberProdTable :: [[Int]]
nimberProdTable = fmap mul <$> [(i,) <$> [0 ..] | i <- [0 ..]]
  where
    mul (a, b) = mex $ [(nimberProdTable !! a' !! b) `nimberAdd` (nimberProdTable !! a !! b') `nimberAdd` (nimberProdTable !! a' !! b') | a' <- [0 .. a - 1], b' <- [0 .. b - 1]]