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 Rust (1.42.0) (judge verdict: Accepted)

pub trait Zero: PartialEq + Sized {
    fn zero() -> Self;
    #[inline]
    fn is_zero(&self) -> bool {
        self == &Self::zero()
    }
}
pub trait One: PartialEq + Sized {
    fn one() -> Self;
    #[inline]
    fn is_one(&self) -> bool {
        self == &Self::one()
    }
}
macro_rules ! zero_one_impls {($ ({$ Trait : ident $ method : ident $ ($ t : ty ) *, $ e : expr } ) * ) => {$ ($ (impl $ Trait for $ t {# [inline ] fn $ method () -> Self {$ e } } ) * ) * } ; }
zero_one_impls ! ({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 , 0 } {Zero zero f32 f64 , 0. } {One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 , 1 } {One one f32 f64 , 1. } );
pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Clone, Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
mod scanner_impls {
    use super::*;
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn new(s: &'a str) -> Self {
            let iter = s.split_ascii_whitespace();
            Self { iter }
        }
        #[inline]
        pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
            <T as IterScan>::scan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
            marker.mscan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
            (0..size)
                .map(|_| <T as IterScan>::scan(&mut self.iter).expect("scan error"))
                .collect()
        }
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
    macro_rules ! iter_scan_impls {($ ($ t : ty ) * ) => {$ (impl IterScan for $ t {type Output = Self ; # [inline ] fn scan <'a , I : Iterator < Item = &'a str >> (iter : & mut I ) -> Option < Self > {iter . next () ?. parse ::<$ t > () . ok () } } ) * } ; }
    iter_scan_impls ! (char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String );
    macro_rules ! iter_scan_tuple_impl {($ ($ T : ident ) * ) => {impl <$ ($ T : IterScan ) ,*> IterScan for ($ ($ T , ) * ) {type Output = ($ (<$ T as IterScan >:: Output , ) * ) ; # [inline ] fn scan <'a , It : Iterator < Item = &'a str >> (_iter : & mut It ) -> Option < Self :: Output > {Some (($ (<$ T as IterScan >:: scan (_iter ) ?, ) * ) ) } } } ; }
    iter_scan_tuple_impl!();
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl ! (A B );
    iter_scan_tuple_impl ! (A B C );
    iter_scan_tuple_impl ! (A B C D );
    iter_scan_tuple_impl ! (A B C D E );
    iter_scan_tuple_impl ! (A B C D E F );
    iter_scan_tuple_impl ! (A B C D E F G );
    iter_scan_tuple_impl ! (A B C D E F G H );
    iter_scan_tuple_impl ! (A B C D E F G H I );
    iter_scan_tuple_impl ! (A B C D E F G H I J );
    iter_scan_tuple_impl ! (A B C D E F G H I J K );
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        _marker: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            <T as IterScan>::scan(&mut self.inner.iter)
        }
    }
}
pub mod marker {
    use super::*;
    use std::{iter::FromIterator, marker::PhantomData};
    #[derive(Debug, Copy, Clone)]
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(<usize as IterScan>::scan(iter)?.checked_sub(1)?)
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Chars;
    impl IterScan for Chars {
        type Output = Vec<char>;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(iter.next()?.chars().collect())
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct CharsWithBase(pub char);
    impl MarkedIterScan for CharsWithBase {
        type Output = Vec<usize>;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                iter.next()?
                    .chars()
                    .map(|c| (c as u8 - self.0 as u8) as usize)
                    .collect(),
            )
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Collect<T: IterScan, B: FromIterator<<T as IterScan>::Output>> {
        size: usize,
        _marker: PhantomData<fn() -> (T, B)>,
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> Collect<T, B> {
        pub fn new(size: usize) -> Self {
            Self {
                size,
                _marker: PhantomData,
            }
        }
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> MarkedIterScan for Collect<T, B> {
        type Output = B;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                (0..self.size)
                    .map(|_| <T as IterScan>::scan(iter).expect("scan error"))
                    .collect::<B>(),
            )
        }
    }
}
#[macro_export]
macro_rules ! min {($ e : expr ) => {$ e } ; ($ e : expr , $ ($ es : expr ) ,+ ) => {std :: cmp :: min ($ e , min ! ($ ($ es ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! chmin {($ dst : expr , $ ($ src : expr ) ,+ ) => {{let x = std :: cmp :: min ($ dst , min ! ($ ($ src ) ,+ ) ) ; $ dst = x ; } } ; }
#[macro_export]
macro_rules ! max {($ e : expr ) => {$ e } ; ($ e : expr , $ ($ es : expr ) ,+ ) => {std :: cmp :: max ($ e , max ! ($ ($ es ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! chmax {($ dst : expr , $ ($ src : expr ) ,+ ) => {{let x = std :: cmp :: max ($ dst , max ! ($ ($ src ) ,+ ) ) ; $ dst = x ; } } ; }
fn main() {
    #![allow(unused_imports, unused_macros)]
    use std::io::{stdin, stdout, BufWriter, Read as _, Write as _};
    let mut _in_buf = Vec::new();
    stdin().read_to_end(&mut _in_buf).expect("io error");
    let _in_buf = unsafe { String::from_utf8_unchecked(_in_buf) };
    let mut scanner = Scanner::new(&_in_buf);
    macro_rules ! scan {() => {scan ! (usize ) } ; (($ ($ t : tt ) ,* ) ) => {($ (scan ! ($ t ) ) ,* ) } ; ([$ t : tt ; $ len : expr ] ) => {(0 ..$ len ) . map (| _ | scan ! ($ t ) ) . collect ::< Vec < _ >> () } ; ([$ t : ty ; $ len : expr ] ) => {scanner . scan_vec ::<$ t > ($ len ) } ; ([$ t : ty ] ) => {scanner . iter ::<$ t > () } ; ({$ e : expr } ) => {scanner . mscan ($ e ) } ; ($ t : ty ) => {scanner . scan ::<$ t > () } ; }
    let _out = stdout();
    let mut _out = BufWriter::new(_out.lock());
    macro_rules ! print {($ ($ arg : tt ) * ) => (:: std :: write ! (_out , $ ($ arg ) * ) . expect ("io error" ) ) }
    macro_rules ! println {($ ($ arg : tt ) * ) => (:: std :: writeln ! (_out , $ ($ arg ) * ) . expect ("io error" ) ) }
    macro_rules! echo {
        ($ iter : expr ) => {
            echo!($iter, '\n')
        };
        ($ iter : expr , $ sep : expr ) => {
            let mut iter = $iter.into_iter();
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    let n = scan!(i64);
    let l = scan!(i64);
    let ans = (l..n + l).sum::<i64>() - (l..n + l).min_by_key(|&x| x.abs()).unwrap_or_default();
    println!("{}", ans);
}