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.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

class Main{

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		int n = sc.nextInt();
		int k = sc.nextInt();
		int[] t = new int[n];
		int[] d = new int[n];

		ArrayList<Pair> pairs = new ArrayList<Pair>();
		for(int i = 0;i < n;i++){
			t[i] = sc.nextInt();
			d[i] = sc.nextInt();
			Pair pair = new Pair();
			pair.from = t[i];
			pair.end = d[i];
			pairs.add(pair);
		}

		Collections.sort(pairs,Comparator.reverseOrder());

		int[] cc = new int[100001];			



		ArrayList<Integer> one = new ArrayList<Integer>();
		ArrayList<Integer> zero = new ArrayList<Integer>();

		cc[pairs.get(0).from]++;			//各寿司について出てきているか判定
		pairs.get(0).from = 1;
		one.add(pairs.get(0).end);

		for(int i = 1;i < n;i++){
			if(cc[ pairs.get(i).from ] > 0){			//すでに最高値がある時
				pairs.get(i).from = 0;
				zero.add(pairs.get(i).end);
			}else{
				cc[pairs.get(i).from]++;				//新しい寿司の中で最高値
				pairs.get(i).from = 1;
				one.add(pairs.get(i).end);
			}

		}
		int	syuruimax = one.size();

		long ans = 0l;
		int syurui = 0;
		PriorityQueue<Integer> queue = new PriorityQueue<Integer>();

		for(int i = 0;i < k;i++){
			ans += pairs.get(i).end;
			if(pairs.get(i).from == 0){			//最大値じゃない時,
				queue.add(pairs.get(i).end);
				zero.remove(0);
			}else{
				syurui++;
				one.remove(0);
			}
		}	


		long[] maxans = new long[syuruimax+1];
		maxans[syurui] = ans;

		while(syurui < k && syurui < syuruimax){
			ans += (long)one.get(0);
			one.remove(0);
			long del =	(long)queue.poll();
			ans -= del;
			syurui++;
			maxans[syurui] = ans;
			if(queue.isEmpty() || one.isEmpty()){
				break;
			}
		}

		for(int i = 0;i <= syuruimax;i++){
			ans = (long)Math.max(ans, maxans[i] + (long)i*i);
		}

		System.out.println(ans);








	}


}

class Pair implements Comparable{
	int from;		//p
	int end;		//y
	int num;
	int bango;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return end - otherpair.end;
	}
}