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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

const chunks = [];
process.stdin.on("data", (chunk) => {
  chunks.push(chunk);
});
process.stdin.on("end", () => {
  const data = Buffer.concat(chunks).toString("utf8");
  const [X, Y] = data
    .trim()
    .split(" ")
    .map((s) => parseInt(s, 10));
  console.log(solve(X, Y) ? "Yes" : "No");
});

// Y min = X * 2
// Y max = X * 4
function solve(X, Y) {
  if (Y % 2 !== 0) return false;
  if (Y < 2 * X) return false;
  if (Y > 4 * X) return false;
  return true;
}