Problem:
Score : 200 points

Problem Statement

You have N apples, called Apple 1, Apple 2, Apple 3, ..., Apple N. The flavor of Apple i is L+i-1, which can be negative.

You can make an apple pie using one or more of the apples. The flavor of the apple pie will be the sum of the flavors of the apples used.

You planned to make an apple pie using all of the apples, but being hungry tempts you to eat one of them, which can no longer be used to make the apple pie.

You want to make an apple pie that is as similar as possible to the one that you planned to make. Thus, you will choose the apple to eat so that the flavor of the apple pie made of the remaining N-1 apples will have the smallest possible absolute difference from the flavor of the apple pie made of all the N apples.

Find the flavor of the apple pie made of the remaining N-1 apples when you choose the apple to eat as above.

We can prove that this value is uniquely determined.

Constraints

2 \leq N \leq 200

-100 \leq L \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N L

Output

Find the flavor of the apple pie made of the remaining N-1 apples when you optimally choose the apple to eat.

Sample Input 1

5 2

Sample Output 1

18

The flavors of Apple 1, 2, 3, 4, and 5 are 2, 3, 4, 5, and 6, respectively. The optimal choice is to eat Apple 1, so the answer is 3+4+5+6=18.

Sample Input 2

3 -1

Sample Output 2

0

The flavors of Apple 1, 2, and 3 are -1, 0, and 1, respectively. The optimal choice is to eat Apple 2, so the answer is (-1)+1=0.

Sample Input 3

30 -50

Sample Output 3

-1044

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Security.Cryptography;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = ReadLineIntSpilit();
            var q = Enumerable.Range(1, n[0]).ToList();

            for (int i = 0; i < n[0]; i++) {
                q[i] = (n[1] +  q[i]) - 1;
            }

            q.Sort();   

            for (int i = 0; i < q.Count(); i++) {
                if(q[i] > 0) {
                    q[i] = 0;
                    break;
                }
            }

            Console.WriteLine(q.Sum());
        }

        //メモ

        //アルゴリズム

        //・全探索解

        /*
         * 例 [A, B, C]
         *
         *  A - B, A - C
         *  B - C
         * 
         *   for (int i = 0; i < n; i++) {
         *  
         *       for (int j = i + 1; j < n; j++) {
         *
         *           array[i], array[j]
         *
         *       }
         *   }
         */

        // ・配列の前後を見る

        /*
         *  例 array[1, 2, 3, 4, 5]
         *  
         *  r = 3;
         * 
         *  array[i - 1] => 1
         *  array[i] => 2
         *  array[i + 1] => 3
         * 
         * //範囲
         * int r = 3;
         * 
         * for(int i = 1; i <= array.Length - r; i++) { }
         * 
         */

        //配列 --------------------

        //降順
        //Array.Sort(h);
        //Array.Reverse(h);

        //合計値
        //array.Sum();

        //最大値
        //List.Sort(); List[Count() - 1] 

        //連続の整数配列を作成
        //
        // 1, 2, 3, 4, 5,..., n
        //var continuous = Enumerable.Range(1, n).ToList();

        //--------------------

        //切り捨て

        //double d = Math.Floor(n);

        //切り上げ

        //double d = Math.Celling(n);

        //kのn乗
        //(int) Math.Pow(k, n);

        //for文の逆
        //for(int i = array.Length - 1; i >= 0; i--) { }

        /// <summary>
        /// 最大公約数
        /// </summary>
        public static long Gcd(long a, long b)
        {
            while (true) {
                if (a < b) { long tmp = b; b = a; a = tmp; }
                if (a % b == 0) return b;
                var x = a;
                a = b;
                b = x % b;
            }
        }

        /// <summary>
        /// 最小公倍数
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public static long Lcm(long a, long b) => a / Gcd(a, b) * b;

        /// <summary>
        /// コンビネーション
        /// </summary>
        static int nCm(int n, int m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * nCm(n - 1, m - 1) / m;
        }

        /// <summary>
        /// 数字配列の重複をカウント
        /// </summary>
        public static int DistinctInt(IEnumerable<int> array)
        {
            var q = array.Distinct().Count();
            return array.Count() - q;
        }

        /// <summary>
        /// 文字配列の重複をカウント
        /// </summary>
        /// <param name="array"></param>
        /// <returns></returns>
        public static int DistinctString(IEnumerable<string> array)
        {
            var q = array.Distinct().Count();
            return array.Count() - q;
        }

        public static string ReadLine() => Console.ReadLine();
        public static int ReadLineInt() => int.Parse(Console.ReadLine());
        public static long ReadLineLongInt() => long.Parse(Console.ReadLine());
        public static string[] ReadLineStringSplit(char a = ' ') => ReadLine().Split(a).ToArray();
        public static int[] ReadLineIntSpilit(char a = ' ') => ReadLine().Split(a).Select(x => int.Parse(x)).ToArray();
        public static long[] ReadLineLongSpilit(char a = ' ') => ReadLine().Split(a).Select(x => long.Parse(x)).ToArray();
        static string[] GetAlphaLowerArray() => new string[] { "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z" };
        static string[] GetAlphaUpperArray() => new string[] { "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z" };
    }
}