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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

import Data.List

isLeg :: Int -> Int -> Int -> Int
isLeg x y legs
  | 2 * x + 4 * y == legs = x + y
  | otherwise = 0

legCount :: Int -> Int -> Int
legCount animals legs =
    sum $ map (\x -> isLeg x (animals - x) legs) [0..animals]

main = do
    [b,c] <- map read . words <$> getLine
    let l = legCount b c
    putStrLn $ if l > 0 then "Yes" else "No"