Problem:
Score : 200 points

Problem Statement

You are given two integers K and S.

Three variable X, Y and Z takes integer values satisfying 0≤X,Y,Z≤K.

How many different assignments of values to X, Y and Z are there such that X + Y + Z = S?

Constraints

2≤K≤2500

0≤S≤3K

K and S are integers.

Input

The input is given from Standard Input in the following format:

K S

Output

Print the number of the triples of X, Y and Z that satisfy the condition.

Sample Input 1

2 2

Sample Output 1

6

There are six triples of X, Y and Z that satisfy the condition:

X = 0, Y = 0, Z = 2

X = 0, Y = 2, Z = 0

X = 2, Y = 0, Z = 0

X = 0, Y = 1, Z = 1

X = 1, Y = 0, Z = 1

X = 1, Y = 1, Z = 0

Sample Input 2

5 15

Sample Output 2

1

The maximum value of X + Y + Z is 15, achieved by one triple of X, Y and Z.

Solution in Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
  val inputs: Seq[String] = scala.io.Source.stdin.getLines().toList
  
  val nums = inputs.head.split(" ").map(_.toInt)

  println(solve(nums(0), nums(1)))

  private def solve(k: Int, s: Int): Int = {
    val max = 3 * k
    if (s == 0 || s == max) {
      return 1
    }

    var ans = 0
    (0 to k).foreach { i =>
      (0 to k).foreach { j =>
        val sum = i + j
        val dis = s - sum
        if (dis <= k && 0 <= dis) {
          ans = ans + 1
        }
      }
    }

    ans
  }
}