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 PHP (5.6.30) (judge verdict: Accepted)

<?php
list($k,$s) = explode(" ",trim(fgets(STDIN)));

if($s == 0){
echo 1;
}elseif($s == $k * 3){
echo 1;
}else{
$ans = 0;
$x = max(0,$s - $k * 2);
while($x <= $k){
$y = max(0,$s - $x - $k);
$ym = min($k,$s - $x);
while($y <= $ym){
$z= $s - $x - $y;
$zm = min($k,$s - $x - $y);
if($z <= $zm){
++$ans;
}
++$y;
}
++$x;
}
echo $ans;
}
?>