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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
namespace AtCoder {
    class MainClass {
        public static void Main(string[] args) { new MainClass().solve(); }
        Scanner cin = new Scanner();

        int K, S;
        void solve() {
            K = cin.nextInt();
            S = cin.nextInt();

            int X, Y, Z,ans=0;
            for (X = K; X >= 0; X--) {
                for (Y = K; Y >= 0; Y--) {
                    Z = S - X - Y;
                    if (0 <= Z && Z <= K)
                        ans++;
                }
            }

            Console.WriteLine(ans);

        }
        class Scanner {
            string[] nextBuffer; int BufferCnt; char[] cs = new char[] { ' ' };
            public Scanner() { nextBuffer = new string[0]; BufferCnt = 0; }
            public string next() {
                if (BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
                string st = Console.ReadLine();
                while (st == "") st = Console.ReadLine();
                nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
                BufferCnt = 0;
                return nextBuffer[BufferCnt++];
            }
            public char nextChar() { return char.Parse(next()); }
            public int nextInt() { return int.Parse(next()); }
            public long nextLong() { return long.Parse(next()); }
            public double nextDouble() { return double.Parse(next()); }
            public string[] array() { return Console.ReadLine().Split(' '); }
            public char[] arrayChar() { return Array.ConvertAll(array(), char.Parse); }
            public int[] arrayInt() { return Array.ConvertAll(array(), int.Parse); }
            public long[] arrayLong() { return Array.ConvertAll(array(), long.Parse); }
            public double[] arrayDouble() { return Array.ConvertAll(array(), double.Parse); }
        }

        class Mathf {
            public int mod = 1000000007;//10^9+7
            public long Pow(long a, long b) {
                if (b == 0) return 1;
                if (b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
                else return Pow(a * a % mod, b / 2) % mod;
            }
            public long Fact(long n) { return n != 0 ? (n % mod * (Fact(n - 1) % mod) % mod) : 1; }
            public long C(long n, long r) {
                if (r == 0 || n == r) return 1;
                else return (Fact(n) % mod * Pow((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
            }
            public int GCD(int a, int b) { if (a < b) Swap(ref a, ref b); return b == 0 ? a : GCD(b, a % b); }
            public int GCD(int[] array) { return array.Aggregate((v, next) => GCD(v, next)); }
            public void Swap<T>(ref T a, ref T b) { T tmp = a; a = b; b = tmp; }
        }
    }
}