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 Control.Monad
import Data.Function
import Data.Char
import Data.List
import Text.Read
import Text.ParserCombinators.ReadPrec

import qualified Data.ByteString.Char8 as B

newtype Pair a b = Pair { getPair :: (a, b) }

instance (Read a, Read b) => Read (Pair a b) where
  readPrec = Pair `dot` (,) <$> readPrec <* get <*> readPrec

instance (Show a, Show b) => Show (Pair a b) where
  show (Pair (a, b)) = show a ++ " " ++ show b

infixr 8 `dot`
dot :: (c -> d) -> (a -> b -> c) -> a -> b -> d
dot = ((.).(.))

main :: IO ()
main = do
  (x, y) <- getPair <$> readLn
  putStrLn $ if solve x y then "Yes" else "No"

solve :: Int -> Int -> Bool
solve x y = or [ 2 * t + 4 * (x - t) == y | t <- [0 .. x] ]