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: Accepted)

object Main {
  def main(args: Array[String]): Unit = {
    import scala.io.StdIn.readLine
    val Array(datX, datY) = readLine.split(" ").map(_.toInt)

    var ans = false
    (0 to datX) foreach {i =>
      val turtle = i
      val crane = datX - i

      if (ans == false) {
        if (turtle * 4 + crane * 2 == datY) ans = true
      }
    }

    println(if(ans) "Yes" else "No")
  }
}