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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

public static partial class Program
{
    public static void Main()
    {
        var ks = CRL().ArrayInts();
        var k = ks[0];
        var s = ks[1];

        var count = 0;
        for (int x = 0; x <= k; x++)
        {
            for (int y = 0; y <= k; y++)
            {
                var z = s - x - y;
                if (z >= 0 && z <= k)
                {
                    count++;
                }
            }
        }

        CWL(count);
    }
}

public static partial class Program
{
    //テンプレここから
    public static int ToInt(this double d) => (int) d;
    public static long ToLong(this double d) => (long) d;
    public static int ToInt(this string str) => int.Parse(str);
    public static long ToLong(this string str) => long.Parse(str);
    public static long[] ToLong(this IEnumerable<string> strs) => strs.Select(x => x.ToLong()).ToArray();
    public static int[] ToInt(this IEnumerable<string> strs) => strs.Select(x => x.ToInt()).ToArray();
    public static long[] ArrayLongs(this string str, char opr = ' ') => str.Split(opr).ToLong();
    public static int[] ArrayInts(this string str, char opr = ' ') => str.Split(opr).ToInt();
    public static string CRL() => Console.ReadLine();
    public static void CWL(object obj) => Console.WriteLine(obj);
    public static long Diff(long a, long b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static int Diff(int a, int b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static long Sign(this long i) => Math.Sign(i);
    public static bool IsEven(this long i) => i % 2 == 0;
    public static bool IsEven(this int i) => i % 2 == 0;
    public static long[] dx = new long[] {0, -1, 0, 1};
    public static long[] dy = new long[] {-1, 0, 1, 0};
    public static long mod = 1000000007;
    public static string alphabet = "abcdefghijklmnopqrstuvwxyz";
    public static long ToLong(this char c) => c.ToString().ToInt();
    public static long[] Sort(this long[] array) => array.OrderBy(x => x).ToArray();
    public static int[] Sort(this int[] array) => array.OrderBy(x => x).ToArray();
    public static long[] DSort(this long[] array) => array.OrderByDescending(x => x).ToArray();
    public static int[] DSort(this int[] array) => array.OrderByDescending(x => x).ToArray();
    public static string Join(this IEnumerable<string> array, string sep = "") => string.Join(sep, array);
    public static string Join(this IEnumerable<char> array, string sep = "") => string.Join(sep, array);
    public static long GCD(long a, long b) => b == 0 ? a : GCD(b, a % b);

    public static long LCM(long a, long b) => a * b / GCD(a, b);

    //テンプレここまで
}