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 = {
    val Array( animals_num, total_foots_num ) = io.StdIn.readLine.split(" ").map{_.toInt}
    var flag = false

    ( 0 to animals_num ).foreach{ i =>
      val turtles_num = animals_num - i
      val cranes_num  = i
      if( turtles_num*4 + cranes_num*2 == total_foots_num ) flag = true
    }

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