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)

rekkyo :: Integer -> Integer -> [(Integer,Integer)]
rekkyo n k = [(x,y)|(x,y) <- doubles n,check(x,y,k,n)]

doubles :: Integer -> [(Integer,Integer)]
doubles n = [(x,y)|x <- [0..n],y <- [0..n]]

check :: (Integer,Integer,Integer,Integer) -> Bool
check(x,y,k,n) =((0 <= k-x-y) && (k-x-y <= n))

main = do
    [n,k] <- map read . words <$> getLine
    let res = rekkyo n k 
    print (length res)