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 os
import numpy as np

if os.path.exists('input.txt'):
    test_mode = True
else:
    test_mode = False

if test_mode:
    f = open('input.txt')
    
def get_input():
    if test_mode:
        return f.readline().rstrip()
    else:
        return input().rstrip()

input_line = get_input().split()
X = int(input_line[0])
Y = int(input_line[1])

kame = float((Y - 2*X)/2)
turu = float(X - kame)

if turu >= 0 and kame >= 0 and turu.is_integer() and kame.is_integer() :
    print('Yes')
else:
    print('No')

if test_mode:
    f.close()