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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php

fscanf(STDIN, "%d %d", $K, $S);

$SUM = $S * 3;
$p = 0;
$flag =false;

if(2 <= $K && $K <= 2500 && 0 <= $S && $S <= 3000) {
    for($x=0; $x<=$K; $x++){
        for($y=0; $y<=$x; $y++){
            $flag = $x ==$y;
            for($z=0; $z<=$y; $z++){
                $s = $x + $y + $z;
                if($s == $S){
                        if($x * $y * $z == $K * $K * $K)
                                $p+=1;
                        elseif($flag or $y == $z or $z == $x)
                                $p+=3;
                        else    $p+=1;
                }
            }
        }
    }
}

echo $p;

?>