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: Accepted)

<?php
/**
 * @see: https://atcoder.jp/contests/abc051/tasks/abc051_b
 */

function getInput(): array
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}

function calculate(int $K, int $S): int
{
    $numberOfTriples = 0;

    for ($X = 0; $X <= min($K, $S); $X++) {
        for ($Y = 0; $Y <= min($K, $S - $X); $Y++) {
            $Z = $S - $X - $Y;

            if (0 <= $Z && $Z <= $K) {
                $numberOfTriples++;
            }
        }
    }

    return $numberOfTriples;
}

list($K, $S) = getInput();

$result = calculate($K, $S);

echo $result . PHP_EOL;