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 LuaJIT (2.0.4) (judge verdict: Accepted)

local K, S = io.read("*n", "*n")

---x >= y >= z
local x, y, z = 0, 0, 0
if K >= S then
	x = S
elseif 2*K >= S then
	x, y = K, S - K
else
	x, y, z = K, K, S - 2*K
end

local count = 0
local sub_x, sub_y, sub_z = x, y, z
while sub_y >= sub_z do
	while y >= z do
		if x == y and y == z then
			count = count + 1
		elseif x == y or y == z then
			count = count + 3
		else
			count = count + 6
		end
		y, z = y - 1, z + 1
	end

	if sub_x == sub_y + 1 then
		sub_x, sub_z = sub_x - 1, sub_z + 1
	elseif x == sub_y then
		sub_x, sub_y, sub_z = sub_x - 1, sub_y - 1, sub_z + 2
	else
		sub_x, sub_y = sub_x - 1, sub_y + 1
	end
	x, y, z = sub_x, sub_y, sub_z
end

print(count)