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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define fio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)
using ll=long long;
using ld=long double;
#define inf INT_MAX  
const ll infll=1ll*inf*inf;
#define mode 998244353
#define mod 1000000007
const long double PI=3.141592653589793238462643383279502884197169399375105820974944;
#define pb push_back
#define mp make_pair
#define ub upper_bound 
#define lb lower_bound 
#define far(i,a,b) for (ll i = a; i <= b; i++)
#define rev(i,a,b) for (ll i = a; i >= b; i--)
#define all(v) v.begin(),v.end()
#define ff first
#define ss second
#define sz(a) int((a).size())
#define ftr(c,i) for(auto i = begin(c); i != end(c); i++)
#define rtr(c,i) for(auto i = rbegin(c); i != rend(c); i++)
#define pre(c,x) ((c).find(x) != (c).end())
#define cpre(c,x) (find(all(c),x) != (c).end())
#define mii map<int,int>
#define mll map<ll,ll>
#define vs vector<string>
#define vi vector<int>
#define vl vector<ll>
#define pll pair<ll,ll>
#define pii pair<int,int>
#define vii vector<pii >
#define vll vector<pll >
#define vvl vector<vector<ll> >
#define vvi vector< vector<int > >
#define wh(t) while(t --)
#define print(arr) for (auto it = arr.begin(); it != arr.end(); ++it) cout <<(ll)(it-arr.begin()) << ')' <<  *it << ' '; cout << endl;
#define printii(arr) for (auto it = arr.begin(); it != arr.end(); ++it) cout << it->ff<<' '<<it->ss << endl; cout << endl;
#define MID(i,j) ((i)+(j))/2
#define nl '\n' 
#define lcm(a,b) ((a)*(b))/gcd((a),(b))
ll max(ll a,ll b) {return (a>b? a:b);}
ll min(ll a,ll b) {return (a>b? b:a);}
ll gcd(ll a,ll b) {return (b==0)? a:gcd(b,a%b); }
ll gcd(ll a,ll b,ll & x,ll & y) {
    if (a == 0) {
        x = 0;
        y = 1;
        return b;
    }
    ll x1, y1;
    ll d = gcd(b % a, a, x1, y1);
    x = y1 - (b / a) * x1;
    y = x1;
    return d;
}
ll modinv(ll a,ll b){
	ll x,y;
	gcd(a, b, x, y);
	return (x%b + b)%b;
}
ll ceiling(ll a,ll b){ 
        if(a%b==0) return a/b;
        else return a/b+1;
}
ll bpow(ll a,ll b,ll m){
	a%=m;
	ll res=1;
	while(b>0){
		if(b&1) res=(res*a)%m;
		b>>=1;
		a=a*a%m;
	}
	return res;
}
vvl mat_mul(vvl mat1,vvl mat2,ll mod1){
        vvl res(sz(mat1),vl(sz(mat2[0]),0));
        far(i,0,sz(mat1)-1){
                far(j,0,sz(mat2[0])-1){
                        far(k,0,sz(mat1[0])-1){
                                res[i][j]=(res[i][j]+(mat1[i][k]*mat2[k][j])%mod1)%mod1;          
                        }   
        }   
        }   
        return res;
}
vvl mat_exp(vvl mat,ll p,ll mod1){ 
        vvl res(sz(mat),vl(sz(mat[0]),0));
        far(i,0,sz(mat)-1) res[i][i]=1;
        while(p>0){
                if(p&1) res=mat_mul(res,mat,mod1);   
                mat=mat_mul(mat,mat,mod1);
                p>>=1;
        }   
        return res;
}
const int N=2*1e5+5;
ll n,m,q,t,k,x,y,z,ans;

int main()
{
	cin >> n >> t;
	if(t<=-n) ans=n;
	else if(t>=1) ans=1;
	else ans=1-t;
	cout << ans << nl;
}