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)

# B - Crane and Turtle
import numpy as np
def is_integer(n):
    try:
        float(n)
    except ValueError:
        return False
    else:
        return float(n).is_integer()
X, Y = map(int, input().split())    
mat = np.array([[2,-0.5],[-1,0.5]])
matb = np.array([[X], [Y]])
Ans = np.dot(mat, matb)
if (is_integer(Ans[0]) is True) and (is_integer(Ans[1]) is True):
    if (Ans[0] >= 0) and (Ans[1] >= 0):
        print("Yes")
    else:
        print("No")
else:
    print("No")