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)

main :: IO ()
main = do
       [x,y] <- (map read . words) <$> getLine
       putStrLn $ solve x y
       
solve :: Int -> Int -> String
solve x y | fold [0..x] y False == True = "Yes"
          | otherwise        = "No"

fold :: [Int] -> Int -> Bool -> Bool
fold _ _ True = True
fold [] _ False = False 
fold (x'@(x:xs)) y False | 2*x + 4*((last x') - x) == y = fold xs y True
                         | otherwise                    = fold xs y False