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.*;
import java.util.*;

public class Main {
	
	static long[] sumLengthOfDigitNumber = new long[19];
	static long[] digit10 = new long[19];
				
	public static void main(String[] args) throws IOException {
		FastScanner sc = new FastScanner(System.in);
		
		int N = sc.nextInt();
		int K = sc.nextInt();
		Pair[] list = new Pair[N];
		for(int i = 0; i < N; i++){
			list[i] = new Pair(sc.nextInt(), sc.nextInt());
		}
		
		Arrays.sort(list, (p1, p2)->p2.d-p1.d);
		
		for(Pair p : list) System.out.println(p.t + " " + p.d);
		
		long ansSum = 0;
		int ansType = 0;
		HashMap<Integer, Long> map = new HashMap<Integer, Long>();
		for(int i = 0; i < K; i++){
			ansSum += list[i].d;
			Long count = map.get(list[i].t);
			if(count == null) map.put(list[i].t, 1L);
			else map.put(list[i].t, count+1);
		}
		ansType = map.size();
		int index = K-1;
		
		long ans = (ansType*ansType + ansSum);
		
		if(K == N){
			System.out.println(ans);
			return;
		}
		
		//System.out.println("\n" + ansSum + " " + ansType + " " + (ansType*ansType + ansSum));
		
		Pair[] nokori = new Pair[N-K];
		for(int i = K; i < N; i++) nokori[i-K] = list[i];
		Arrays.sort(nokori, (p1, p2)->p1.compTD(p2));
		//for(Pair p : nokori) System.out.println(p.t + " " + p.d);
		for(Pair p : nokori){
			
			Long count = map.get(p.t);
			if(count != null) continue;
			//System.out.println("type" + " " + p.t);
			while(index >= 0){
				if(list[index].t != p.t){
					long sum = ansSum - list[index].d + p.d;
					int type = ansType + 1;
					long res = (type*type + sum);
					//System.out.println(sum + " " + type + " " + res);
					ansSum = sum;
					ansType = type;
					ans = Math.max(ans, res);
					index--;
					
					map.put(p.t, 1L);
					break;
				}else{
					
				}
			}
			if(map.size() == K) break;
		}
		
		System.out.println(ans);
		
	}//end main
	
}//end Main

class Pair{
	int t, d;
	public Pair(int t, int d){
		this.t = t; this.d = d;
	}
	
	public int compTD(Pair p){
		if(this.d != p.d){
			return p.d - this.d;
		}else{
			return p.t - this.t;
		}
	}
}

class FastScanner {
    private InputStream in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(InputStream in) {
		this.in = in;
	}
    private 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;
    }
    private int readByte() {
    	if (hasNextByte()) return buffer[ptr++];
    	else return -1;
    }
    private static boolean isPrintableChar(int c){
    	return 33 <= c && c <= 126;
    }
    public boolean hasNext() {
    	while(hasNextByte() && !isPrintableChar(buffer[ptr]))
    		ptr++; return hasNextByte();
    }
    public 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();
    }
    public 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();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
}