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 Python (3.8.2) (judge verdict: Wrong Answer)

x, y = input().split()
x = int(x)
y = int(y)

def check(x, y):
    # 動物の可能性を考える
    for i in range(0, x):
        # 2本足,4本足の動物の数
        leg2_animal = i+1
        leg4_animal = x - leg2_animal
        
        # 全体の足の数を数えてみる
        sum_legs = leg2_animal * 2 + leg4_animal * 4

        if sum_legs == y:
            print("Yes")
            return

    print("No")

check(x,y)