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 Lua (5.3.2) (judge verdict: Accepted)

local k, s = io.read("*n", "*n")
local ret = (s + 2) * (s + 1) // 2
if k + 1 <= s then
  local a = s - (k + 1)
  ret = ret - 3 * (a + 2) * (a + 1) // 2
end
if 2 * (k + 1) <= s then
  local a = s - 2 * (k + 1)
  ret = ret + 3 * (a + 2) * (a + 1) // 2
end
if 3 * (k + 1) <= s then
  local a = s - 3 * (k + 1)
  ret = ret - (a + 2) * (a + 1) // 2
end
print(ret)