Problem:
Score : 200 points

Problem Statement

There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs.

Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct.

Constraints

1 \leq X \leq 100

1 \leq Y \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

If there is a combination of numbers of cranes and turtles in which the statement is correct, print Yes; otherwise, print No.

Sample Input 1

3 8

Sample Output 1

Yes

The statement "there are 3 animals in total in the garden, and they have 8 legs in total" is correct if there are two cranes and one turtle. Thus, there is a combination of numbers of cranes and turtles in which the statement is correct.

Sample Input 2

2 100

Sample Output 2

No

There is no combination of numbers of cranes and turtles in which this statement is correct.

Sample Input 3

1 2

Sample Output 3

Yes

We also consider the case in which there are only cranes or only turtles.

Solution in Scala (2.13.1) (judge verdict: Wrong Answer)

object Main extends App {
  val inputs: Seq[String] = scala.io.Source.stdin.getLines().toList

  val nums = inputs.head.split(" ").map(_.toInt)
  val animals = nums(0)
  val legs    = nums(1)

  println(solve(animals, legs))

  def solve(animals: Int, legs: Int): String = {
    // 足の数が奇数の場合false
    if (legs % 2 != 0) {
      return "No"
    }

    val kame = legs / 4
    val bird = legs / 2

    if ((kame to bird).contains(animals)) {
      return "Yes"
    }
    return "No"
  }
}