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.Char
import Data.List

solve :: Int -> Int -> Int
solve k s = solver 0 0
    where　solver x y
            | y > k = 0
            | x > k = 0
            | x == 0 = solver 0 (y+1) + solver 1 y + if (s-y)>=0 && (s-y) <= k then 1 else 0
            | otherwise = solver (x+1) y + if (s-x-y)>=0 && (s-x-y) <= k then 1 else 0

main = do
    [k,s] <- (map read . words) <$> getLine
    print $ solve k s