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: Time Limit Exceeded)


import java.util.ArrayList;
import java.util.Collections;
import java.util.HashSet;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Set;

public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int N = Integer.parseInt(scan.next());
		int K = Integer.parseInt(scan.next());
		int[] t = new int[N];
		long[] d = new long[N];
		Sushi sushi = null;
		Set<Integer> kindSet = new HashSet<>();
		PriorityQueue<Sushi> sushiQueue = new PriorityQueue<>(Collections.reverseOrder());
		for (int i = 0; i < N; i++) {
			sushi = new Sushi(Integer.parseInt(scan.next()), Integer.parseInt(scan.next()));
			sushiQueue.add(sushi);
			kindSet.add(sushi.getT());
		}

		int maxKind = kindSet.size();

		SushiList S = new SushiList(N);
		//K個の寿司を貪欲にSに格納
		for (int i = 0; i < K; i++) {
			S.add(sushiQueue.poll());
		}

		if (S.getKindNum() == maxKind) { //種類がこれ以上増えないなら終わり
			System.out.println(S.getScore());
			return;
		}

		long max = S.getScore();
		for (int i = S.getKindNum(); i <= maxKind; i++) {
			if (S.getMinSushi() == null) {
				System.out.println(Math.max(max, S.score));
				return;
			}
			S.remove(S.getMinSushi());
			while (!sushiQueue.isEmpty()) {
				if (!S.kindList.contains(sushiQueue.peek().getT())) {
					S.add(sushiQueue.poll());
					break;
				} else {
					sushiQueue.poll();
				}
			}
			max = Math.max(max, S.score);
		}
		System.out.println(max);
	}

	public static class SushiList {
		private int N;
		private List<Integer> kindList;
		private int kindNum; //種類数
		private long score;
		private Sushi minSushi;
		private PriorityQueue<Sushi>[] sushiArray; //種類ごとの寿司キュー

		public SushiList(int N) {
			this.N = N;
			kindList = new ArrayList<>();
			int kindNum = 0;
			score = 0;
			minSushi = null;
			sushiArray = new PriorityQueue[N + 1];
			for (int i = 0; i < N + 1; i++) {
				sushiArray[i] = new PriorityQueue<Sushi>();
			}
		}

		public void add(Sushi sushi) {
			sushiArray[sushi.getT()].add(sushi);
			if (sushiArray[sushi.getT()].size() > 1) {
				if (minSushi == null) { //初めて重複が出たとき
					minSushi = sushiArray[sushi.getT()].peek();
				} else {
					if (minSushi.getD() > sushiArray[sushi.getT()].peek().getD()) {
						minSushi = sushi;
					}
				}
			}
			kindList.add(sushi.getT());
			score += sushi.getD();
			if (sushiArray[sushi.getT()].size() == 1) {
				score += kindNum * 2 + 1; //p種類からp+1種類に増えるときの差分を足す
				kindNum++;
			}
		}

		public void remove(Sushi sushi) {
			kindList.remove(new Integer(sushi.getT()));
			score -= sushi.getD();
			sushiArray[sushi.getT()].remove(sushi);
			//minSushiの更新
			minSushi = null;
			for (int i = 0; i < N + 1; i++) {
				if (sushiArray[i].size() > 1) {
					if (minSushi == null) {
						minSushi = sushiArray[i].peek();
					} else {
						if (minSushi.getD() > sushiArray[i].peek().getD()) {
							minSushi = sushiArray[i].peek();
						}
					}
				}
			}
		}

		public Sushi getMinSushi() {
			return minSushi;
		}

		public void setMinSushi(Sushi minSushi) {
			this.minSushi = minSushi;
		}

		public long getScore() {
			return score;
		}

		public void setScore(int score) {
			this.score = score;
		}

		public int getKindNum() {
			return kindNum;
		}

		public void setKindNum(int kindNum) {
			this.kindNum = kindNum;
		}
	}

	public static class Sushi implements Comparable<Sushi> {
		private int t;
		private long d;

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

		public boolean isSameType(Sushi s) {
			return this.t == s.getT();
		}

		public int getT() {
			return t;
		}

		public void setT(int t) {
			this.t = t;
		}

		public long getD() {
			return d;
		}

		public void setD(long d) {
			this.d = d;
		}

		@Override
		public int compareTo(Sushi other) {
			return (int) (this.d - other.d);
		}

	}
}