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: Wrong Answer)

x, y = gets.split.map(&:to_i)
 
ans = 'No'
 
if (y/6)*2 + ((y%6)/4) + (((y%6)%4)/2) == x
  ans = 'Yes'
elsif (y/6)*2 + ((y%6)/4) + (((y%6)%4)/2) > x
  sum = (y/6)*2 + ((y%6)/4) + (((y%6)%4)/2) 
  ((y/6)+((y%6)%4)/2).times{|i|
    if sum - (i+1) == x
      ans = 'yes'
    end
    }
elsif (y/6)*2 + ((y%6)/4) + (((y%6)%4)/2) < x
  sum = (y/6)*2 + ((y%6)/4) + (((y%6)%4)/2) 
  ((y/6)+(y%6)/4).times{|j|
    if sum + (j+1) == x
      ans = 'yes'
    end
    }
end
 
puts ans