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 5.4.1) (judge verdict: Wrong Answer)


#pragma warning(disable:4996)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <float.h>

#pragma region 定義
#define i_cin(X) scanf("%d", &X)
#define i_cin2(X,Y) scanf("%d %d",&X,&Y)
#define i_cin3(X,Y,Z) scanf("%d %d %d",&X,&Y,&Z)
#define l_cin(X) scanf("%ld",&X)
#define f_cin(X) scanf("%f",&X)
#define l_cin2(X,Y) scanf("%ld %ld",&X,&Y)
#define s_cin(X) scanf("%s",&X)

#define  i_cout(X) printf("%d\n",X)
#define  f_cout(X) printf("%g\n",X)
#define  i_cout2(X,Y) printf("%d %d\n",X,Y)
#define  l_cout(X) printf("%ld\n",X)
#define  s_cout(X) printf("%s\n",X)
#define  ll_cout(X) printf("%lld\n",X)

typedef long long  ll;
#define rept(x, s, n) for (int x = s; x < n; x++)

#define Yes_RTN s_cout("Yes");return 0
#define No_RTN  s_cout("No");return 0
#define YES_RTN s_cout("YES");return 0
#define NO_RTN  s_cout("NO");return 0


int i_cins(int n, int* A);
int l_cins2(int n, long* A, long* B);
int s_dsort(const void* a, const void* b);
int s_asort(const void* a, const void* b);

int  _gcd(int a, int b);

int s_asorts(const void* a, const void* b);

//昇順
int s_asorts(const void* a, const void* b) {
	return(strcmp((char*)a, (char*)b));
}
int s_dsort(const void* a, const void* b) {
	return(*(int*)b - *(int*)a);
}
int s_asort(const void* a, const void* b) {
	return(*(int*)a - *(int*)b);
}
int l_cins2(int n, long* a, long* b) {
	int i;
	rept(i, 0, n) {
		l_cin2(*(a + i), *(b + i));
	}
	return 0;
}
int i_cins(int n, int* a) {
	int i;
	for (i = 0; i < n; i++) {
		i_cin(*(a + i));
	}

	return 0;
}
int _gcd(int a, int b) {
	int r, tmp;
	if (a < b) { tmp = a; a = b; b = tmp; }
	r = a % b;
	while (r) {
		if (!r) break;
		a = b; b = r;
		r = a % b;
	}
	return(b);
}

long _max(long a, long b) {
	return a > b ? a : b;
}
long _min(long a, long b) {
	return a < b ? a : b;
}

#pragma endregion



int main(void) {
	int N, L;
	int i = 0, tmp = 0, zero = 0;


	i_cin2(N, L);

	for (i = 0; i < N; i++) {
		tmp += (L + i);
	}
	if (!tmp) { i_cout(0); return 0; }
	if (L > 0) { i_cout(tmp - L); return 0; }
	if (L < 0 && tmp>0) { i_cout(tmp); return 0; }
	i_cout(tmp+abs(L)-N+1);
	return 0;
}