class Rational(x: Int, y: Int) {
    require(y != 0, "Denominator must be non-zero")
    private val g = gcd(x, y)
    def numer = x / g
    def denom = y / g

    def + (that: Rational) =
        new Rational(numer * that.denom + that.numer * denom, denom * that.denom)

    def - (that: Rational) = this + (-that)

    def * (that: Rational) = new Rational(numer * that.numer, denom * that.denom)

    def / (that: Rational) = this * (that.inv)

    def inv() = new Rational(denom, numer)

    def unary_- = new Rational(-numer, denom)

    def toDouble() = numer.toDouble / denom.toDouble

    override def toString() =
        (if (numer < 0 || denom < 0) "-" else "") + abs(numer) + "/" + abs(denom)

    private def abs(n: Int) = if (n < 0) -n else n

    private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b)
}