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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import "fmt"

var x, y int

func main() {
	fmt.Scan(&x, &y)

	if y%2 != 0 {
		fmt.Println("No")

	} else {
		if cal(0, 0) {
			fmt.Println("Yes")
		} else {
			fmt.Println("No")
		}
	}
}

func cal(iter int, sum int) bool {

	if sum > y {
		return false
	}

	if iter == x {
		if sum == y {
			return true
		}
		return false
	}

	if cal(iter+1, sum+4) {
		return true
	}
	if cal(iter+1, sum+2) {
		return true
	}

	return false
}