Crane and Turtle

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.

Examples

Input

3 8

Output

Yes

Input

2 100

Output

No

Input

1 2

Output

Yes

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

X Y

outputFormat

Output

If there is a combination of numbers of cranes and turtles in which the statement is correct, print Yes; otherwise, print No.

Examples

Input

3 8

Output

Yes

Input

2 100

Output

No

Input

1 2

Output

Yes

样例

1 2

Yes