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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

main :: IO ()
main = do
  [k,s] <- map read . words <$> getLine :: IO [Int]
  let z_xpy = zip [0..k] [xpy | z <- [0..k], let xpy = s-z]
  let yz = [(y, z) | y <- [0..k], (z, xpy) <- z_xpy, xpy - y >= 0]
  let x = [a |(y, z) <- yz, let a = s-z-y, a >=0 && a<= k]
  print $ length x