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 Ruby (2.3.3) (judge verdict: Wrong Answer)

def C(n,k)
  k = n - k if n - k < k 
  k.times.inject(1){|s,i| s * (n - i) / (i + 1) }
end
K, S = gets.split.map(&:to_i)
ans = (0..3).inject(0) do |t, i|
  sign = i.even? ? 1 : -1
  n = S + 3 - (K + 1) * i - 1
  n >= 3 ? t + sign * C(n, 2) * C(3, i) : t
end
puts ans