Scala solution for maximum-sum-path

sealed trait Tree

case object Empty extends Tree

case class Node(value: Int, left: Tree = Empty, right: Tree = Empty) extends Tree

object Tree {
  def maxPath(tree: Tree): (Seq[Node], Int) = {
      tree match {
        case Empty => (Seq[Node](), 0)
        case node @ Node(value, left, right) =>
          val rl = maxPath(left)
          val rr = maxPath(right)
          val rm = if (rl._2 > rr._2) rl else rr
          (node +: rm._1, node.value + rm._2)
    }
  }
}