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: Wrong Answer)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
//! https://github.com/hatoo/competitive-rust-snippets
//!
//! MIT License
//!
//! Copyright (c) 2018 hatoo
//!
//! Permission is hereby granted, free of charge, to any person obtaining a copy
//! of this software and associated documentation files (the "Software"), to deal
//! in the Software without restriction, including without limitation the rights
//! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
//! copies of the Software, and to permit persons to whom the Software is
//! furnished to do so, subject to the following conditions:
//!
//! The above copyright notice and this permission notice shall be included in all
//! copies or substantial portions of the Software.
//!
//! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
//! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
//! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
//! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
//! SOFTWARE.
#![allow(
    unused_imports,
    unused_attributes,
    unused_macros,
    dead_code,
    non_snake_case
)]
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::{stdin, stdout, BufWriter, Write};
use std::iter::FromIterator;
#[macro_export]
macro_rules ! get {(@ inner [$ src : expr ] chars ) => {{let mut buf = String :: new () ; $ src . read_line (& mut buf ) . unwrap () ; buf . trim () . chars () . collect ::< Vec < char >> () } } ; (@ inner [$ src : expr ] usize1 ) => {{get ! (@ inner [$ src ] usize ) - 1 } } ; (@ inner [$ src : expr ] [usize1 ] ) => {{get ! (@ inner [$ src ] [usize ] ) . into_iter () . map (| v | v - 1 ) . collect ::< Vec < usize >> () } } ; (@ inner [$ src : expr ] [[usize1 ] ; $ n : expr ] ) => {{(0 ..$ n ) . map (| _ | get ! (@ inner [$ src ] [usize1 ] ) ) . collect ::< Vec < _ >> () } } ; (@ inner [$ src : expr ] [usize1 ; $ n : expr ] ) => {{(0 ..$ n ) . map (| _ | get ! (@ inner [$ src ] [usize1 ] ) ) . flatten () . collect ::< Vec < _ >> () } } ; (@ inner [$ src : expr ] [[chars ] ; $ n : expr ] ) => {{(0 ..$ n ) . map (| _ | get ! (@ inner [$ src ] chars ) ) . collect ::< Vec < _ >> () } } ; (@ inner [$ src : expr ] [chars ; $ n : expr ] ) => {{(0 ..$ n ) . map (| _ | get ! (@ inner [$ src ] chars ) ) . collect ::< Vec < _ >> () } } ; (@ inner [$ src : expr ] [($ ($ tt : tt ) ,* ) ; $ n : expr ] ) => {{(0 ..$ n ) . map (| _ | get ! (@ inner [$ src ] ($ ($ tt ) ,* ) ) ) . collect ::< Vec < _ >> () } } ; (@ inner [$ src : expr ] ($ ($ tt : tt ) ,* ) ) => {{let mut buf : String = String :: new () ; $ src . read_line (& mut buf ) . unwrap () ; let mut iter = buf . split_whitespace () ; ($ (get ! (@ inner_elem_parse [$ tt ] iter . next () . unwrap () ) , ) * ) } } ; (@ inner [$ src : expr ] [$ t : ty ] ) => {{let mut buf = String :: new () ; $ src . read_line (& mut buf ) . unwrap () ; buf . trim () . split_whitespace () . map (| t | t . parse ::<$ t > () . unwrap () ) . collect ::< Vec < _ >> () } } ; (@ inner [$ src : expr ] [[$ t : ty ] ; $ n : expr ] ) => {{(0 ..$ n ) . map (| _ | get ! (@ inner [$ src ] [$ t ] ) ) . collect ::< Vec < _ >> () } } ; (@ inner [$ src : expr ] [$ t : ty ; $ n : expr ] ) => {{(0 ..$ n ) . map (| _ | get ! (@ inner [$ src ] [$ t ] ) ) . flatten () . collect ::< Vec < _ >> () } } ; (@ inner [$ src : expr ] $ t : ty ) => {{let mut buf = String :: new () ; $ src . read_line (& mut buf ) . unwrap () ; buf . trim () . split_whitespace () . next () . unwrap () . parse ::<$ t > () . unwrap () } } ; (@ inner_elem_parse [usize1 ] $ elem : expr ) => {{get ! (@ inner_elem_parse [usize ] $ elem ) - 1 } } ; (@ inner_elem_parse [$ t : ty ] $ elem : expr ) => {{$ elem . parse ::<$ t > () . unwrap () } } ; ($ tt : tt ) => {{use std :: io :: BufRead ; let get_stdin = std :: io :: stdin () ; let mut locked_stdin = get_stdin . lock () ; get ! (@ inner [& mut locked_stdin ] $ tt ) } } ; }
macro_rules ! debug {($ ($ a : expr ) ,* $ (, ) * ) => {# [cfg (debug_assertions ) ] eprintln ! (concat ! ($ ("| " , stringify ! ($ a ) , "={:?} " ) ,*, "|" ) , $ (&$ a ) ,* ) ; } ; }
macro_rules ! echo {($ ($ a : expr ) ,* ) => {let mut s = Vec :: new () ; $ (s . push (format ! ("{}" , $ a ) ) ; ) * println ! ("{}" , s . join (" " ) ) ; } }
#[macro_export]
macro_rules ! chmin {($ base : expr , $ ($ cmps : expr ) ,+ $ (, ) * ) => {{let cmp_min = min ! ($ ($ cmps ) ,+ ) ; if $ base > cmp_min {$ base = cmp_min ; true } else {false } } } ; }
#[macro_export]
macro_rules ! chmax {($ base : expr , $ ($ cmps : expr ) ,+ $ (, ) * ) => {{let cmp_max = max ! ($ ($ cmps ) ,+ ) ; if $ base < cmp_max {$ base = cmp_max ; true } else {false } } } ; }
#[macro_export]
macro_rules ! min {($ a : expr $ (, ) * ) => {{$ a } } ; ($ a : expr , $ b : expr $ (, ) * ) => {{std :: cmp :: min ($ a , $ b ) } } ; ($ a : expr , $ ($ rest : expr ) ,+ $ (, ) * ) => {{std :: cmp :: min ($ a , min ! ($ ($ rest ) ,+ ) ) } } ; }
#[macro_export]
macro_rules ! max {($ a : expr $ (, ) * ) => {{$ a } } ; ($ a : expr , $ b : expr $ (, ) * ) => {{std :: cmp :: max ($ a , $ b ) } } ; ($ a : expr , $ ($ rest : expr ) ,+ $ (, ) * ) => {{std :: cmp :: max ($ a , max ! ($ ($ rest ) ,+ ) ) } } ; }
const BIG_STACK_SIZE: bool = true;
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
fn solve() {
    use std::cmp::Reverse;
    let (n, k) = get!((usize, usize));
    let mut td = get!([(usize1, usize); n]);
    td.sort_by_key(|&(_, d)| Reverse(d));

    let mut sum_d = 0;
    let mut appear_count = vec![0; n];
    let mut kinds = 0;
    let mut min_heap = BinaryHeap::new();
    for i in 0..k {
        let (t, d) = td[i];
        if appear_count[t] == 0 {
            kinds += 1;
        }
        appear_count[t] += 1;
        min_heap.push((Reverse(d), t));
        sum_d += d;
    }
    let mut not_used_d = HashMap::new();
    for (t, d) in td {
        if appear_count[t] != 0 {
            continue;
        }
        not_used_d
            .entry(t)
            .and_modify(|e| {
                if *e < d {
                    *e = d;
                }
            })
            .or_insert(d);
    }
    let mut not_used_max_heap = BinaryHeap::new();
    for (_, d) in not_used_d {
        not_used_max_heap.push(d);
    }

    let mut ans = sum_d + kinds * kinds;
    while let Some(unused_max_d) = not_used_max_heap.pop() {
        kinds += 1;

        while let Some((Reverse(min_d), t)) = min_heap.pop() {
            if appear_count[t] >= 2 {
                appear_count[t] -= 1;
                sum_d -= min_d;
                sum_d += unused_max_d;
                break;
            }
        }

        chmax!(ans, kinds * kinds + sum_d);
    }

    echo!(ans);
}
*/

fn main() {
    let exe = "/tmp/bin01B04251";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";