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 1.1.14) (judge verdict: Accepted)

(defun count-pairs (k s)
  (let ((mx (if (>= k s)
              s
              k))
        (mn (if (>= k s)
              0
              (- s k))))
    (if (<= mn mx)
      (+ (- mx mn) 1)
      0)))

(defun solv (k s)
    (loop for i below (+ k 1)
        sum (count-pairs k (- s i))))
 
(defparameter k (read))
(defparameter s (read))
(defparameter ans (solv k s))
(princ ans)