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: Wrong Answer)

module Main where

import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

import Data.Maybe (fromJust)
import qualified Data.ByteString.Char8 as BS
bytestr2Int = fst . fromJust . BS.readInt
getInt = bytestr2Int <$> BS.getLine
getIntL_H = map bytestr2Int. BS.words <$> BS.getLine
getIntL_V n = replicate n $ getInt
getInt2D n = replicate n $ getIntL_H

data Curr = Zero
          | One Int
          | Two Int Int
          | Filled Int Int Int
          deriving (Show)

main :: IO ()
main = do
    [k,s] <- getIntL_H
    print $ check k s 0 Zero

check k s a c =
    if k<a then
        []
    else case c of
        Zero -> next c (One a)
        (One x) -> next c (Two x a)
        (Two x y) -> if a==s
            then
                next c (Filled x y a)
            else
                check k s (a+1) c
        _ -> [c]
    where
        next rm ad = check k s (a+1) rm ++ check k (s-a) 0 ad