Why does foldr function with three arguments?

I looked at some list operations and came across !!

:

(!!)                    :: [a] -> Int -> a
xs !! n
  | n < 0     = negIndex
  | otherwise = foldr (\x r k -> case k of
                                   0 -> x
                                   _ -> r (k-1)) tooLarge xs n

      

        
        
        
      

    

A function (\x r k -> ...)

has a type a -> (Int -> a) -> Int -> a

, but it foldr

accepts a function that must take only two arguments:

foldr            :: (a -> b -> b) -> b -> [a] -> b
foldr k z = go
          where
            go []     = z
            go (y:ys) = y `k` go ys

      

        
        
        
      

    

Can someone explain to me why it foldr

takes a function that takes 3 arguments with the following type a -> (Int -> a) -> Int -> a

? Moreover, the result must be of the same type as the second argument?