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 Python (3.8.2) (judge verdict: Accepted)

import sys
import numpy as np
def I(): return int(sys.stdin.readline().rstrip())
def IL(): return map(int,sys.stdin.readline().rstrip().split())

def Main():
    x,y = IL()
    a = np.matrix([
        [1,1],
        [2,4]
    ])
    b = np.matrix([
        [x],
        [y]
    ])
    ans = np.linalg.solve(a,b)
    if np.all(0<=ans) and np.all(abs(ans-np.round(ans)<1e-5)):
        print('Yes')
    else:
        print('No')
    return

if __name__=='__main__':
    Main()