Problem:
Score : 400 points

Problem Statement

There are N pieces of sushi. Each piece has two parameters: "kind of topping" t_i and "deliciousness" d_i.
You are choosing K among these N pieces to eat.
Your "satisfaction" here will be calculated as follows:

The satisfaction is the sum of the "base total deliciousness" and the "variety bonus".

The base total deliciousness is the sum of the deliciousness of the pieces you eat.

The variety bonus is x*x, where x is the number of different kinds of toppings of the pieces you eat.

You want to have as much satisfaction as possible.
Find this maximum satisfaction.

Constraints

1 \leq K \leq N \leq 10^5

1 \leq t_i \leq N

1 \leq d_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
t_1 d_1
t_2 d_2
.
.
.
t_N d_N

Output

Print the maximum satisfaction that you can obtain.

Sample Input 1

5 3
1 9
1 7
2 6
2 5
3 1

Sample Output 1

26

If you eat Sushi 1,2 and 3:

The base total deliciousness is 9+7+6=22.

The variety bonus is 2*2=4.

Thus, your satisfaction will be 26, which is optimal.

Sample Input 2

7 4
1 1
2 1
3 1
4 6
4 5
4 5
4 5

Sample Output 2

25

It is optimal to eat Sushi 1,2,3 and 4.

Sample Input 3

6 5
5 1000000000
2 990000000
3 980000000
6 970000000
6 960000000
4 950000000

Sample Output 3

4900000016

Note that the output may not fit into a 32-bit integer type.

Solution in Rust (1.15.1) (judge verdict: Accepted)

pub trait FromFragments: Sized {
    fn fragments_count() -> usize;
    fn from_fragments(fragments: &[&str]) -> Result<Self, String>;
}
impl FromFragments for () {
    fn fragments_count() -> usize {
        1
    }
    fn from_fragments(_fragments: &[&str]) -> Result<(), String> {
        Ok(())
    }
}
impl FromFragments for String {
    fn fragments_count() -> usize {
        1
    }
    fn from_fragments(fragments: &[&str]) -> Result<String, String> {
        Ok(fragments[0].to_string())
    }
}
macro_rules ! impl_from_fragments { ( $ ( $ t : ty ) * ) => { $ ( impl FromFragments for $ t { fn fragments_count ( ) -> usize { 1 } fn from_fragments ( fragments : & [ & str ] ) -> Result <$ t , String > { use std :: str :: FromStr ; <$ t >:: from_str ( fragments [ 0 ] ) . map_err ( | _ | { format ! ( "cannot parse \"{}\" as {}" , fragments [ 0 ] , stringify ! ( $ t ) ) } ) } } ) * } ; }
impl_from_fragments ! ( isize usize i8 u8 i16 u16 i32 u32 i64 u64 f32 f64 ) ;
pub trait FromLine: Sized {
    fn from_line(line: &str) -> Result<Self, String>;
}
fn split_into_fragments(line: &str) -> Vec<&str> {
    line.trim_right_matches('\n').split_whitespace().collect()
}
impl<T: FromFragments> FromLine for T {
    fn from_line(line: &str) -> Result<T, String> {
        let fragments = split_into_fragments(line);
        if fragments.len() != T::fragments_count() {
            return Err(format!(
                "line \"{}\" has {} fragments, expected {}",
                line,
                fragments.len(),
                T::fragments_count()
            ));
        }
        T::from_fragments(&fragments)
    }
}
impl<T: FromFragments> FromLine for Vec<T> {
    fn from_line(line: &str) -> Result<Vec<T>, String> {
        let n = T::fragments_count();
        let fragments = split_into_fragments(line);
        if fragments.len() % n != 0 {
            return Err(format!(
                "line \"{}\" has {} fragments, expected multiple of {}",
                line,
                fragments.len(),
                n
            ));
        }
        let mut result = Vec::new();
        for chunk in fragments.chunks(n) {
            match T::from_fragments(chunk) {
                Ok(v) => result.push(v),
                Err(msg) => {
                    let flagment_msg = if n == 1 {
                        format!("fragment {}", result.len())
                    } else {
                        let l = result.len();
                        format!("fragments {}-{}", n * l + 1, (n + 1) * l)
                    };
                    return Err(format!("{} of line \"{}\": {}", flagment_msg, line, msg));
                }
            }
        }
        Ok(result)
    }
}
macro_rules ! impl_from_fragments_for_tuples { ( $ t : ident $ var : ident $ count : expr ) => ( ) ; ( $ t : ident $ var : ident $ count : expr ; $ ( $ inner_t : ident $ inner_var : ident $ inner_count : expr ) ;* ) => { impl_from_fragments_for_tuples ! ( $ ( $ inner_t $ inner_var $ inner_count ) ;* ) ; impl <$ t : FromFragments , $ ( $ inner_t : FromFragments ) ,*> FromFragments for ( $ t , $ ( $ inner_t ) ,* ) { fn fragments_count ( ) -> usize { let mut n = <$ t >:: fragments_count ( ) ; $ ( n += <$ inner_t >:: fragments_count ( ) ; ) * n } # [ allow ( unused_assignments ) ] fn from_fragments ( fragments : & [ & str ] ) -> Result < ( $ t , $ ( $ inner_t ) ,* ) , String > { let mut start = 0 ; let $ var = <$ t >:: from_fragments ( & fragments [ start .. start +<$ t >:: fragments_count ( ) ] ) ?; start += <$ t >:: fragments_count ( ) ; $ ( let $ inner_var = <$ inner_t >:: from_fragments ( & fragments [ start .. start +<$ inner_t >:: fragments_count ( ) ] ) ?; start += <$ inner_t >:: fragments_count ( ) ; ) * Ok ( ( $ var , $ ( $ inner_var ) ,* ) ) } } } }
impl_from_fragments_for_tuples ! ( T4 x4 4 ; T3 x3 3 ; T2 x2 2 ; T1 x1 1 ) ;
#[macro_export]
macro_rules ! read { ( ) => { let mut line = String :: new ( ) ; std :: io :: stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; } ; ( $ pat : pat = $ t : ty ) => { let mut line = String :: new ( ) ; std :: io :: stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; let $ pat = <$ t >:: from_line ( & line ) . unwrap ( ) ; } ; ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { read ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ) ; } ; }
#[macro_export]
macro_rules ! readls { ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { $ ( read ! ( $ pat = $ t ) ; ) * } }
pub fn read_vec<T: FromLine>() -> Vec<T> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin
        .lock()
        .lines()
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::from_line(&line).unwrap()
        })
        .collect();
    result
}
#[macro_export]
macro_rules ! read_loop { ( $ pat : pat = $ t : ty ; $ block : block ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; for line in stdin . lock ( ) . lines ( ) { let line = line . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: from_line ( & line ) . unwrap ( ) ; $ block } } ; ( $ ( $ pat : pat = $ t : ty ) ,* ; $ block : block ) => { read_loop ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ; $ block ) ; } }
#[macro_export]
macro_rules ! readn_loop { ( $ n : expr ; $ pat : pat = $ t : ty ; $ block : block ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; { let lock = stdin . lock ( ) ; for _ in 0 ..$ n { let line = String :: new ( ) ; lock . read_line ( & mut line ) . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: from_line ( & line ) . unwrap ( ) ; $ block } } } ; ( $ n : expr ; $ ( $ pat : pat = $ t : ty ) ,* ; $ block : block ) => { read_times_loop ! ( $ n ; ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ; $ block ) ; } }

#[derive(Clone)]
pub struct LScan<I: Iterator, S: Clone, F: FnMut(S, I::Item) -> S> {
    iter: I,
    state: Option<S>,
    f: F,
}

impl<I: Iterator, S: Clone, F: FnMut(S, I::Item) -> S> Iterator for LScan<I, S, F> {
    type Item = S;

    fn next(&mut self) -> Option<S> {
        if self.state.is_none() {
            return None;
        }

        let state_inner = self.state.take().unwrap();
        if let Some(item) = self.iter.next() {
            let cloned = state_inner.clone();
            self.state = Some((self.f)(cloned, item));
        }

        Some(state_inner)
    }
}

#[derive(Clone)]
pub struct StepBy<I> {
    iter: I,
    step: usize,
    first_take: bool,
}
impl<I: Iterator> Iterator for StepBy<I> {
    type Item = I::Item;
    fn next(&mut self) -> Option<Self::Item> {
        if self.first_take {
            self.first_take = false;
            self.iter.next()
        } else {
            self.iter.nth(self.step)
        }
    }
}
trait RichIterator: Iterator {
    fn step_by_(self, step: usize) -> StepBy<Self>
    where
        Self: Sized,
    {
        assert_ne!(step, 0);
        StepBy {
            iter: self,
            step: step - 1,
            first_take: true,
        }
    }
    fn for_each<F: FnMut(Self::Item)>(self, mut f: F)
    where
        Self: Sized,
    {
        for item in self {
            f(item);
        }
    }

    fn lscan<S: Clone, F: FnMut(S, Self::Item) -> S>(self, state: S, f: F) -> LScan<Self, S, F>
    where
        Self: Sized,
    {
        LScan {
            iter: self,
            state: Some(state),
            f: f,
        }
    }
}
impl<I: Iterator> RichIterator for I {}

#[derive(Debug)]
struct Sushi {
    t: usize,
    d: i64,
}

impl FromFragments for Sushi {
    fn fragments_count() -> usize {
        2
    }
    fn from_fragments(fs: &[&str]) -> Result<Sushi, String> {
        Ok(Sushi {
            t: usize::from_fragments(&fs[0..1])? - 1,
            d: i64::from_fragments(&fs[1..2])?,
        })
    }
}

use std::collections::HashSet;

fn main() {
    read!(_n = usize, k = usize);
    let mut sushis: Vec<Sushi> = read_vec();
    sushis.sort_by(|s1, s2| s2.d.cmp(&s1.d));

    let mut is_t_taken = HashSet::new();
    let mut taken_ds = Vec::new();
    let mut left_ds = Vec::new();
    for sushi in sushis {
        if !is_t_taken.contains(&sushi.t) && taken_ds.len() < k {
            is_t_taken.insert(sushi.t);
            taken_ds.push(sushi.d);
        } else {
            left_ds.push(sushi.d);
        }
    }

    let taken_cumsum: Vec<_> = taken_ds.iter().lscan(0, |a, b| a + b).collect();
    let left_cumsum: Vec<_> = left_ds.iter().lscan(0, |a, b| a + b).collect();
    let ans = (1..taken_ds.len() + 1)
        .filter(|i| (k - i) <= left_ds.len())
        .map(|i| taken_cumsum[i] + left_cumsum[k - i] + (i * i) as i64)
        .max()
        .unwrap();
    println!("{}", ans);
}