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 Kotlin (1.3.71) (judge verdict: Accepted)

fun main(args: Array<String>) {
  val (X, Y) = readInts()
  for (i in 0..X) {
    val a = i
    val b = X - i
    val n = a * 2 + b * 4
    if (n == Y) {
      println("Yes")
      return
    }
  }
  println("No")
}

fun myBinarySearch(begin: Int, end: Int, isOk: (key: Int) -> Boolean): Int {
  var ng = begin
  var ok = end

  while (Math.abs(ok - ng) > 1) {
    val mid = (ok + ng) / 2
    if (isOk(mid)) {
      ok = mid
    } else {
      ng = mid
    }
  }

  return ok
}

fun <T> List<T>.myBinarySearch(isOk: (T) -> Boolean): Int {
  return myBinarySearch(-1, size) { index -> isOk(get(index)) }
}

fun <T> Array<T>.myBinarySearch(isOk: (T) -> Boolean): Int {
  return myBinarySearch(-1, size) { index -> isOk(get(index)) }
}

fun readString() = readLine()!!
fun readStrings() = readString().split(" ")
fun readInt() = readString().toInt()
fun readLong() = readString().toLong()
fun readInts() = readStrings().map { it.toInt() }
fun readLongs() = readStrings().map { it.toLong() }