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 Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(declaim (optimize (speed 3) (debug 0) (safety 0)))
(let ((k (read))
      (s (read)))

  (declare (type fixnum k))
  (declare (type fixnum s))

  (format t "~A~%"
          (loop for i from 0 to k
                sum (loop for j from 0 to k
                          count (and (>= (the fixnum (- s i j)) 0) (<= (the fixnum (- s i j)) k))))))