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++ (GCC 9.2.1) (judge verdict: Accepted)



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  **╚═════╝░╚══════╝╚═╝░░╚═╝░░░╚═╝░░░╚═╝░╚════╝░░╚═════╝░**
  *********************************************************/

#include <bits/stdc++.h>
using namespace std;


#define ll                          long long
#define ld                          long double

#define forn(i,n)                   for(int i=0;i<n;++i)
#define all(v)                      v.begin(), v.end()
#define rall(v)                     v.rbegin(),v.rend();
#define isSubstring(s1,s2)          s1.find(s2) != std::string::npos
	
#define pb                          push_back
#define pf                          push_front
#define mp                          make_pair
#define fr                          first
#define sc                          second

#define vpi                         <vector<pair<int,int>>
#define vi                          vector<int>
#define sz(a)                       (int)a.size()

#define   endl                       "\n"
#define     nl                       cout<<"\n";
#define fastio                       ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);

#define MN                           INT_MIN
#define MX                           INT_MAX

bool isPrime(ll n){if(n<2)return false;for(ll x = 2;x*x <=n;x++){if(n%x == 0)return false;}return true;}
bool isPerfectSquare(long double x){long double sr=sqrt(x);return((sr-floor(sr))==0);}
int gcd(int a, int b){if(a==0)return b;if(b==0) return a;if(a==b)return a;if(a>b)return gcd(a-b,b);return gcd(a,b-a);} 


int32_t main()
{
	int n,l;
	cin >> n >> l;
	int s = 0;
	for(int i = 1;i<= n;i++)
	{
		s += i+ l - 1;
	}
	int minabs = 100000;
	int rem;
	for(int i= 1;i<= n;i++)
	{
		if(minabs > abs(i+l-1))
		{
			rem = i;
			minabs = abs(i+l-1);
		}
	}
	cout << s - (l + rem - 1) << endl;
}