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 Ruby (2.7.1) (judge verdict: Accepted)

def turukame(a, b, num, remain)
  y = (remain - a * num) / (b - a)
  x = num - y

  return [-1, -1] if remain != a * x + b * y
  return [-1, -1] if y < 0 || x < 0

  [x, y]
end

X, Y = gets.split.map(&:to_i)

a, b = turukame(2, 4, X, Y)

if a < 0 || b < 0
  puts 'No'
else
  puts 'Yes'
end