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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)



import java.util.AbstractMap;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;

public class Main {

	static Scanner scanner;

	public static void main(String[] args) {
	    scanner = new Scanner(System.in);

	    int N=gi();
	    int K=gi();
	    int[] T=new int[N];
	    long[] D=new long[N];
	    Pair<Long, Integer>[] ps=new Pair[N];
	    int[] used=new int[N];
	    for(int i=0; i<N;i++) {
	    	int t=gi()-1;
	    	long d=gl();
	    	ps[i]=new Pair<Long, Integer>(d, t);
	    }

	    Arrays.parallelSort(ps, Collections.reverseOrder());

	    long k=0;
	    long point=0;
	    long max=0;
	    for(int i=0; i<K;i++) {
	    	Pair<Long, Integer> p = ps[i];
	    	if(used[p.getValue()]==0)k++;
	    	used[p.getValue()]++;
	    	point+=p.getKey();
	    }

	    point+=Math.pow(k, 2);
	    max=point;

	    for(int i=K; i<N;i++) {
	    	Pair<Long, Integer> p = ps[i];
	    	if(used[p.getValue()]==0) {
	    	    used[p.getValue()]++;
	    	    point-=Math.pow(k, 2);
	    	    k++;
	    	    point+=Math.pow(k, 2);
	    	    point+=p.getKey();
	    	    for(int j=K-1; j>=0;j--) {
	    	    	if(used[ps[j].getValue()]>1) {
	    	    		used[j]--;
	    	    		point-=ps[j].getKey();
	    	    		break;
	    	    	}
	    	    }
	    	    max=Math.max(max, point);
	    	}
	    }

	    System.out.print(max);
	}

	public static class Pair<K, V> extends AbstractMap.SimpleEntry<K, V> implements Comparable<Pair<K, V>> {
		/** serialVersionUID. */
	    private static final long serialVersionUID = 6411527075103472113L;

	    public Pair(final K key, final V value) {
	        super(key, value);
	    }

		@Override
		public int compareTo(Pair<K, V> o) {

			Comparable key = (Comparable)this.getKey();
			Comparable key2 = (Comparable)o.getKey();

			return key.compareTo(key2);
		}

	}

	// 文字列として入力を取得
	public static String gs() {
		return scanner.next();
	}

	// intとして入力を取得
	public static int gi() {
		return Integer.parseInt(scanner.next());
	}

	// longとして入力を取得
	public static long gl() {
		return Long.parseLong(scanner.next());
	}

	// doubleとして入力を取得
	public static double gd() {
		return Double.parseDouble(scanner.next());
	}
}