Hackerrank `Day of the Programmer` problem

DayOfTheProgrammer.scala

import scala.io._

trait Date {
  def toDDMMYYYY: String = ???
}
case class ConcreteDate(day: Int, month: String, year: Int) extends Date {
  override def toDDMMYYYY = s"$day.$month.$year"
}
case object EmptyDate extends Date

object DayOfTheProgrammer {
  val months = List(("01", 31), ("02", 28), ("03", 31), ("04", 30), ("05", 31), ("06", 30), 
    ("07", 31), ("08", 31), ("09", 30), ("10", 31), ("11", 30), ("12", 31))

  private def isJulianLeap(year: Int): Boolean = year % 4 == 0
  private def isGregorianLeap(year: Int): Boolean = (year % 400 == 0) || (year % 4 == 0 && year % 100 != 0)

  def dayOfProgrammer(year: Int): String = {
    lazy val isLeapJulian = isJulianLeap(year)
    lazy val isLeapGregorian = isGregorianLeap(year)

    val dayOfProgrammer = months.foldLeft((EmptyDate, 256): Tuple2[Date, Int])((acc, month) => {
      val daysRemaining = acc._2
      val currentDate = acc._1
      val monthName = month._1

      val daysInMonth = if (monthName == "02") {
        if (year < 1918 && isLeapJulian ) month._2 + 1
        else if (year > 1918 && isLeapGregorian) month._2 + 1
        else if (year == 1918) month._2 - (if (isLeapGregorian) 12 else 13)
        else month._2
      } else month._2

      if (daysRemaining == 0) acc
      else if (daysRemaining < daysInMonth) (ConcreteDate(daysRemaining, monthName, year), 0)
      else (ConcreteDate(daysInMonth, monthName, year), daysRemaining - daysInMonth)
    })._1

    dayOfProgrammer.toDDMMYYYY
  }

  def main(args: Array[String]): Unit = {
    val year = StdIn.readLine.trim.toInt
    val result = dayOfProgrammer(year)

    println(result)
  }
}