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.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
import java.util.TreeSet;

public class Main implements Runnable { // クラス名はMain1

	PrintWriter out = new PrintWriter(System.out);
	InputReader sc = new InputReader(System.in);

	public static void main(String[] args) {
		Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1));
		new Thread(null, new Main(), "", 1024 * 1024 * 1024).start(); // 16MBスタックを確保して実行
	}

	public void run() {

		try {
			int N = sc.nextInt();
			int K = sc.nextInt();
			Sushi[] s = new Sushi[N];
			for (int i = 0; i < N; i++) {
				//A[i] = sc.nextInt();
				Sushi sushi = new Sushi();
				sushi.t = sc.nextInt();
				sushi.d = sc.nextInt();
				sushi.count = 1;
				s[i] = sushi;
			}

			Arrays.sort(s, new Comparator<Sushi>() {
				@Override
				public int compare(Sushi o1, Sushi o2) {
					if (o1.t == o2.t) {
						return o2.d - o1.d;
					} else {
						return o1.t - o2.t;
					}
				}
			});

			/*
			for (int i = 0; i < N; i++) {
				out.println("t:" + s[i].t + " ,d:" + s[i].d + " ,cnt:" + s[i].count);
			}
			*/

			for (int i = 1; i < N; i++) {
				if (s[i].t == s[i - 1].t) {
					s[i].count = s[i - 1].count + 1;
				}
			}

			Arrays.sort(s, new Comparator<Sushi>() {
				@Override
				public int compare(Sushi o1, Sushi o2) {
					if (o1.d == o2.d) {
						return o1.count - o2.count;
					} else {
						return o2.d - o1.d;
					}
				}
			});

			/*
			for (int i = 0; i < N; i++) {
				out.println("t:" + s[i].t + " ,d:" + s[i].d + " ,cnt:" + s[i].count);
			}
			*/

			PriorityQueue<Sushi> pq = new PriorityQueue<>();
			TreeSet<Integer> ts = new TreeSet<>();
			long kiso = 0;
			long type = 0;
			for (int i = 0; i < K; i++) {
				pq.offer(s[i]);
				kiso += s[i].d;
				ts.add(s[i].t);
			}
			type = ts.size() * ts.size();

			long ans = kiso + type;

			for (int i = K; i < N; i++) {
				if (!ts.contains(s[i].t)) {
					if (pq.peek().count > 1) {
						Sushi es = pq.poll();
						long nextkiso = kiso - es.d + s[i].d;
						long nexttype = (ts.size() + 1) * (ts.size() + 1);
						kiso = nextkiso;
						ts.add(s[i].t);
						type = ts.size() * ts.size();
						pq.add(s[i]);
						ans = Math.max(ans, kiso + type);
					}
				}
			}

			out.println(ans);
			//Flushしてからcloseするのが無難
			out.flush();
			out.close();

		} catch (ArithmeticException ae) {
			ae.printStackTrace();
			throw new RuntimeException();
		} catch (Exception e) {
			e.printStackTrace();
			throw new RuntimeException();
		}

	}

	class Sushi implements Comparable<Sushi> {

		public int t;
		public int d;
		public int count;

		@Override
		public int compareTo(Sushi o) {
			if (this.count >= 2) {
				return this.d - o.d;
			} else {
				return o.count - this.count;
			}
		}

	}

	// 高速なScanner
	static class InputReader {
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

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

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

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

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}