Immutable stream batching

Is there an immutable alternative to the solution in this question, which batches up data in a stream:

val records =
  Source(List(
    Record(1, "a"),
    Record(1, "k"),
    Record(1, "k"),
    Record(1, "a"),
    Record(2, "r"),
    Record(2, "o"),
    Record(2, "c"),
    Record(2, "k"),
    Record(2, "s"),
    Record(3, "!")
  ))
  .concat(Source.single(Record(0, "notused"))) // needed to print the last element

records
  .statefulMapConcat { () =>
    var currentTime = 0
    var payloads: Seq[String] = Nil

    record =>
      if (record.time == currentTime) {
        payloads = payloads :+ record.payload
        Nil
      } else {
        val previousState = (currentTime, payloads)
        currentTime = record.time
        payloads = Seq(record.payload)
        List(previousState)
      }
  }
  .runForeach(println)

Produces

(0,List())
(1,List(a, k, k, a))
(2,List(r, o, c, k, s))
(3,List(!))