import scala.collection.mutable.ArrayBuffer
 
object Main extends App {
 
  class Rational(val p: BigInt, val q: BigInt) {
 
    def +(that: Rational) = Rational(p * that.q + q * that.p, q * that.q)
 
    def *(that: Rational) = Rational(p * that.p, q * that.q)
 
    def toDouble = p.toDouble / q.toDouble
 
    override def toString = s"$p/$q"
  }
 
  object Rational {
    def apply(p: BigInt, q: BigInt): Rational = {
      require(q != 0)
      val d = p gcd q
      new Rational(p / d, q / d)
    }
 
    def apply(n: BigInt): Rational = Rational(n, 1)
  }
 
  val l = ArrayBuffer(Rational(1))
  for (n <- 1 to 100)
    l += l.last * Rational(100 - n, 100)
 
  println((1 to 100).map(n => (n, (l(n - 1) * Rational(n, 100)).toDouble)).maxBy(_._2))
}
 

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