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 Kotlin (1.3.71) (judge verdict: Accepted)

import kotlin.system.exitProcess

fun main(args: Array<String>) {
    val (x, y) = readLine()!!.split(" ").map { it.toInt() }

    // 鶴:a, 亀:bと仮定
    // x =  a +  b
    // y = 2a + 4b
    // -> y = 2x + 2b
    //    b を0からxの範囲でループして検証

    for (b in 0..x) {
        if (y == 2 * x + 2 * b) {
            print("Yes")
            exitProcess(0)
        }
    }

    print("No")
}