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: Wrong Answer)


import math


X,Y=map(int, input().split())
if math.isclose(-Y//2+2*X, math.ceil(-Y//2+2*X)) and math.isclose(Y//2-X, math.ceil(Y//2-X)):
    if Y//2-X>0 and -Y//2+2*X>0:
        print("Yes")


    elif Y//2-X==0 and -Y//2+2*X>0:
         print("Yes")


    elif Y//2-X>0 and -Y//2+2*X==0:
         print("Yes")

    else:
         print("No")


else:
    print("No")