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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.util.NoSuchElementException;

import java.io.InputStream;

import java.io.PrintWriter;

import java.util.PriorityQueue;

class Sushi implements Comparable<Sushi> {
    // ネタ おいしさ
    int t;
    int d;

    Sushi(int t, int d) {
        this.t = t;
        this.d = d;
    }

    // x.compereTo(y)
    // 降順
    // x は d
    // y は Sushi.d
    @Override
    public int compareTo(Sushi sushi) {
        return sushi.d - this.d;
    }
}

@SuppressWarnings("unchecked")
public class Main {
    static PriorityQueue<Integer>[] sushiList;
    static PriorityQueue<Integer>[] sushiTmp;

    static PriorityQueue<Sushi> s;
    static PriorityQueue<Sushi> sTmp;

    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);

        final int N = nextInt();
        final int K = nextInt();

        // 降順
        s = new PriorityQueue<>();
        sTmp = new PriorityQueue<>();

        int kind = 0;

        for (int i = 0; i < N; i++) {
            // 0-indexed
            int t = nextInt() - 1;
            int d = nextInt();

            Sushi sushi = new Sushi(t, d);
            s.add(sushi);
            kind = Math.max(kind, t);
        }

        kind++;

        sushiList = new PriorityQueue[kind];
        sushiTmp = new PriorityQueue[kind];

        // 昇順
        for (int i = 0; i < kind; i++) {
            sushiList[i] = new PriorityQueue<>();
            sushiTmp[i] = new PriorityQueue<>();
        }

        boolean[] done = new boolean[kind];

        long cnt = 0;
        long deli = 0;

        for (int i = 0; i < K; i++) {
            Sushi x = s.poll();

            // 0-indexed
            sushiList[x.t].add(x.d);

            deli += x.d;

            // 0-indexed
            if (!done[x.t]) {
                done[x.t] = true;
                cnt++;
            }
        }

        long ans = deli + cnt * cnt;

        for (int i = 0; i < kind; i++) {
            long tmpcnt = 0;
            long curdeli = deli;

            while (done[i] && 1 < sushiList[i].size()) {
                int num = Math.min(s.size(), sushiList[i].size() - 1);

                for (int j = 0; j < num; j++) {
                    int a = sushiList[i].poll();

                    Sushi b = s.poll();

                    if (!done[b.t]) {
                        done[b.t] = true;

                        tmpcnt++;
                        curdeli = curdeli - a + b.d;

                        long curcnt = cnt + tmpcnt;

                        if (ans < curdeli + curcnt * curcnt) {
                            sushiTmp[i].clear();

                            deli = curdeli;
                            cnt = curcnt;

                            ans = deli + cnt * cnt;

                            tmpcnt = 0;

                            sushiList[b.t].add(b.d);

                            while (0 < sTmp.size()) {
                                Sushi c = sTmp.poll();
                                sushiList[c.t].add(c.d);
                            }
                        } else {
                            sushiTmp[i].add(a);
                            sTmp.add(b);
                        }
                    }
                }
            }

            while (0 < sushiTmp[i].size()) {
                int x = sushiTmp[i].poll();
                sushiList[i].add(x);
            }

            while (0 < sTmp.size()) {
                Sushi x = sTmp.poll();
                done[x.t] = false;
                s.add(x);
            }
        }

        out.println(ans);

        out.flush();
    }

    // FastScanner start
    static final InputStream in = System.in;
    static final byte[] buffer = new byte[1024];
    static int ptr = 0;
    static int buflen = 0;

    static boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    static int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    static boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    static String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    static long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    static int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    static double nextDouble() {
        return Double.parseDouble(next());
    }
    // FastScanner end
}