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 OCaml (4.02.3) (judge verdict: Accepted)

let () = Scanf.scanf "%d %d" @@ fun k s ->
  Printf.printf "%d\n" @@
  if 3 * k < s
  then 0
  else
    Array.fold_left ( + ) 0 @@
    Array.init (1 + min s k) @@ fun x ->
      Array.fold_left ( + ) 0 @@ Array.init (1 + min (s - x) k) @@ fun y ->
        if s - x - y <= k then 1 else 0