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: Wrong Answer)

{-# LANGUAGE PartialTypeSignatures #-}
{-# LANGUAGE LambdaCase #-}
module Main (main) where

import qualified Data.ByteString.Char8 as C8

import qualified Data.Char as C
import qualified Data.List as L

main :: IO ()
main = readInts >>= output . solve

solve :: [Int] -> _
solve [1,y] = y==2 || y==4
solve [x,y] = not $ null [ True | k1 <- [2..x], k2 <- [1..x-k1-1], (k1*2)+(k2*4)==y]

output :: _ -> IO ()
output = \case
  True -> putStrLn "Yes"
  False -> putStrLn "No"

-- utils
readInts :: IO [Int]
readInts = L.unfoldr (C8.readInt . C8.dropWhile C.isSpace) <$> C8.getLine