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)

x, y = gets.chomp.split(" ").map(&:to_i)

# 鶴の数:a  亀の数:b
#  a +  b =  x
# 2a + 4b =  y
    #   a = ( 4x - y) / 2
    #   b = (-2x + y) / 2

# a, b が0以上の正の整数でなければ不正？
# c, d が 0 ならば a, b は整数
#       c = ( 4x - y) % 2
#       d = (-2x + y) % 2
c = (4 * x - y) % 2
d = (-2 * x + y) % 2

a = (4 * x - y) / 2
b = (-2 * x + y) / 2

if c == 0 && d == 0 && a >= 0 && b >= 0
    puts "Yes"
else
    puts "No"
end