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)

import Data.Maybe (fromJust)
import qualified Data.ByteString.Char8 as B

solve :: Int -> Int -> Int -> Int -> Int -> Int
solve i j t k s
    | i > s || i > k = t
    | j - i > k || j > s = solve (i + 1) (i + 1) t k s
    | s - j > k = solve i (j + 1) t k s
    | otherwise = solve i (j + 1) (t + 1) k s

main :: IO ()
main = do
    [k, s] <- map (fst . fromJust . B.readInt) . B.words <$> B.getLine :: IO [Int]
    print $ solve 0 0 0 k s