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: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

namespace codeTester.contest190622
{
    class ProblemB
    {
        static List<int> values = new List<int>();
        static long answer = 0;

        public static void Main(string[] args)
        {
            Input();
            Logic();
            Output();
        }

        static void Input()
        {
            values = ReadSpaceSeparatedValues();
        }

        public static List<int> ReadSpaceSeparatedValues()
        {
            List<int> values = new List<int>();
            string[] inputs = Console.ReadLine().Split(' ');
            foreach (string input in inputs)
            {
                values.Add(int.Parse(input));
            }

            return values;
        }

        static void Logic()
        {
            int n = values[0];
            int l = values[1];
            long origTaste = n * (n - 1) / 2 + n * l;
            // i に L を足して 1 を引いた値の絶対値が最小なやつだから
            // i - 1 の値が、負かつ絶対値が N 以下ならば、i - 1 の絶対値番目のリンゴを食べて、味に変化なし
            // i - 1 の値が、負でないならば、1 つ目のリンゴを食べて、その分味が変化
            // i - 1 の値が、負かつ絶対値が N 以上ならば、n 番目のリンゴを食べて、その分味が変化
            int threshold = l - 1;
            if (threshold >= 0)
            {
                answer = origTaste - l;
                return;
            }
            if (Math.Abs(threshold) > n)
            {
                answer = origTaste - l - n + 1;
                return;
            }
            answer = origTaste;
        }

        static void Output()
        {
            Console.WriteLine(answer.ToString());
        }
    }
}