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: Wrong Answer)

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

// TYPEDEF
// ----------------------------------------
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> Pair;
typedef vector<ll> vll;
typedef vector<vector<ll>> Graph;
typedef vector<string> vs;
typedef vector<pair<ll, ll>> Pll;
typedef queue<ll> qll;

// REPEAT
// ----------------------------------------
#define REP(i,n) for(ll i=0;i<(ll)(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define REPA(i,a) for(ll i=0;i<(ll)(a.size());i++);
#define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define FORD(i,a,b) for(ll i=a;i>=(ll)(b);i--)
#define COUT(a) cout << (a) << endl;
#define ENDL(a) cout << endl;
#define COUTA(i,a) for(ll i=0;i<(ll)(a.size());i++) {cout << (a)[i] << " ";} cout << endl;

// UTIL
// ----------------------------------------
#define pb push_back
#define paired make_pair
#define ALL(a) (a).begin(),(a).end()
#define SORT(a) sort((a).begin(),(a).end())
#define RSORT(a) sort((a).rbegin(), (a).rend())

// DEBUG
// ----------------------------------------
#ifdef _DEBUG
#define debug(x) cout << "[debug] " << #x << ": " << x << endl
#else
#define debug(x)
#endif

template <typename T>
void debugV(const vector<T> v) {
#ifdef _DEBUG
  rep(i, v.size()) {
    cout << i << ":" << v[i] << " ";
  }
  cout << endl;
#else
  (void)v;
#endif
}

// BIT FLAG
// ----------------------------------------
const unsigned int BIT_FLAG_0 = (1 << 0); // 0000 0000 0000 0001
const unsigned int BIT_FLAG_1 = (1 << 1); // 0000 0000 0000 0010
const unsigned int BIT_FLAG_2 = (1 << 2); // 0000 0000 0000 0100
const unsigned int BIT_FLAG_3 = (1 << 3); // 0000 0000 0000 1000
const unsigned int BIT_FLAG_4 = (1 << 4); // 0000 0000 0001 0000
const unsigned int BIT_FLAG_5 = (1 << 5); // 0000 0000 0010 0000
const unsigned int BIT_FLAG_6 = (1 << 6); // 0000 0000 0100 0000
const unsigned int BIT_FLAG_7 = (1 << 7); // 0000 0000 1000 0000
const unsigned int BIT_FLAG_8 = (1 << 8); // 0000 0001 0000 0000
const unsigned int BIT_FLAG_9 = (1 << 9); // 0000 0010 0000 0000
const unsigned int BIT_FLAG_10 = (1 << 10); // 0000 0100 0000 0000
const unsigned int BIT_FLAG_11 = (1 << 11); // 0000 1000 0000 0000

// CONST
// ----------------------------------------
constexpr ll INF = 0x3f3f3f3f3f3f3f3f;
constexpr double PI=3.14159265358979323846; // or M_PI
constexpr int MOD = 1000000007;


void Main() {
    ll n, l;
    cin >> n >> l;
    ll total = 0;
    ll min_apple = INF;
    REP(i, n) {
      min_apple = min(min_apple, abs(i + l));
      total += i + l;
    }

    COUT(total - min_apple);
}

int main()
{
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	cout << fixed << setprecision(15);
	Main();
}

/*

5
1 3 5 4 2
*/