Problem:
Score : 1200 points

Problem Statement

There are N jewels, numbered 1 to N.
The color of these jewels are represented by integers between 1 and K (inclusive), and the color of Jewel i is C_i.
Also, these jewels have specified values, and the value of Jewel i is V_i.

Snuke would like to choose some of these jewels to exhibit.
Here, the set of the chosen jewels must satisfy the following condition:

For each chosen jewel, there is at least one more jewel of the same color that is chosen.

For each integer x such that 1 \leq x \leq N, determine if it is possible to choose exactly x jewels, and if it is possible, find the maximum possible sum of the values of chosen jewels in that case.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq K \leq \lfloor N/2 \rfloor

1 \leq C_i \leq K

1 \leq V_i \leq 10^9

For each of the colors, there are at least two jewels of that color.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
C_1 V_1
C_2 V_2
:
C_N V_N

Output

Print N lines.
In the i-th line, if it is possible to choose exactly i jewels, print the maximum possible sum of the values of chosen jewels in that case, and print -1 otherwise.

Sample Input 1

5 2
1 1
1 2
1 3
2 4
2 5

Sample Output 1

-1
9
6
14
15

We cannot choose exactly one jewel.

When choosing exactly two jewels, the total value is maximized when Jewel 4 and 5 are chosen.

When choosing exactly three jewels, the total value is maximized when Jewel 1, 2 and 3 are chosen.

When choosing exactly four jewels, the total value is maximized when Jewel 2, 3, 4 and 5 are chosen.

When choosing exactly five jewels, the total value is maximized when Jewel 1, 2, 3, 4 and 5 are chosen.

Sample Input 2

5 2
1 1
1 2
2 3
2 4
2 5

Sample Output 2

-1
9
12
12
15

Sample Input 3

8 4
3 2
2 3
4 5
1 7
3 11
4 13
1 17
2 19

Sample Output 3

-1
24
-1
46
-1
64
-1
77

Sample Input 4

15 5
3 87
1 25
1 27
3 58
2 85
5 19
5 39
1 58
3 12
4 13
5 54
4 100
2 33
5 13
2 55

Sample Output 4

-1
145
173
285
318
398
431
491
524
576
609
634
653
666
678

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.ArrayList;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.Objects;
import java.util.List;
import java.io.Writer;
import java.security.AccessControlException;
import java.io.BufferedReader;
import java.util.regex.Pattern;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        FJewels solver = new FJewels();
        solver.solve(1, in, out);
        out.close();
    }

    static class FJewels {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            Debug.autoEnable();
            int n = in.ints(), k = in.ints();
            FJewels.JewelSet[] jewels = new FJewels.JewelSet[k];
            for (int i = 0; i < k; i++) {
                jewels[i] = new FJewels.JewelSet(i);
            }
            boolean odd = false;
            for (int i = 0; i < n; i++) {
                int col = in.ints() - 1;
                jewels[col].values.add(in.longs());
                if (jewels[col].values.size() >= 3) {
                    odd = true;
                }
            }
            for (int i = 0; i < k; i++) {
                jewels[i].values.sort(Comparator.reverseOrder());
            }

            Arrays.sort(jewels, Comparator.comparing(j -> -j.top2()));
            PriorityQueue<Long> single = new PriorityQueue<>(Comparator.reverseOrder());
            long ans = jewels[0].top2();
            jewels[0].addRemain(single);

            List<Long> ansEven = new ArrayList<>(n);
            ansEven.add(ans);
            int c = 1;

            for (int i = 4; i <= n; i += 2) {
                if (single.size() < 2) {
                    ans += jewels[c].top2();
                    ansEven.add(ans);
                    jewels[c].addRemain(single);
                    c++;
                    continue;
                } else if (c == k) {
                    long s1 = single.poll(), s2 = single.poll();
                    ans += s1 + s2;
                    ansEven.add(ans);
                    continue;
                }
                long pair = jewels[c].top2();
                long s1 = single.poll(), s2 = single.poll();
                if (pair >= s1 + s2) {
                    ans += pair;
                    single.offer(s1);
                    single.offer(s2);
                    jewels[c].addRemain(single);
                    c++;
                } else {
                    ans += s1 + s2;
                }
                ansEven.add(ans);
            }


            if (!odd) {
                for (int i = 1; i <= n; i++) {
                    if (i % 2 == 0) {
                        out.ans(ansEven.get((i - 1) / 2)).ln();
                    } else {
                        out.ans(-1).ln();
                    }
                }
                return;
            }

            ans = -1;
            int ansi = -1;
            for (int i = 0; i < k; i++) {
                if (ans < jewels[i].top3()) {
                    ans = jewels[i].top3();
                    ansi = i;
                }
            }
            List<Long> ansOdd = new ArrayList<>(n);
            ansOdd.add(-1L);
            ansOdd.add(ans);

            single.clear();
            jewels[ansi].addRemain(single);
            single.poll();


            c = 0;
            for (int i = 5; i <= n; i += 2) {
                if (c == ansi) {
                    c++;
                }
                if (single.size() < 2) {
                    ans += jewels[c].top2();
                    ansOdd.add(ans);
                    jewels[c].addRemain(single);
                    c++;
                    continue;
                } else if (c == k) {
                    long s1 = single.poll(), s2 = single.poll();
                    ans += s1 + s2;
                    ansOdd.add(ans);
                    continue;
                }
                long pair = jewels[c].top2();
                long s1 = single.poll(), s2 = single.poll();
                if (pair >= s1 + s2) {
                    ans += pair;
                    single.offer(s1);
                    single.offer(s2);
                    jewels[c].addRemain(single);
                    c++;
                } else {
                    ans += s1 + s2;
                }
                ansOdd.add(ans);
            }

            for (int i = 1; i <= n; i++) {
                if (i % 2 == 0) {
                    out.ans(ansEven.get((i - 1) / 2)).ln();
                } else {
                    out.ans(ansOdd.get(i / 2)).ln();
                }
            }

        }

        private static class JewelSet {
            int type;
            List<Long> values = new ArrayList<>();

            public JewelSet(int type) {
                this.type = type;
            }

            public long top2() {
                return values.get(0) + values.get(1);
            }

            public long top3() {
                if (values.size() < 3) {
                    return -1;
                }
                return values.get(0) + values.get(1) + values.get(2);
            }

            public void addRemain(PriorityQueue<Long> q) {
                for (int i = 2; i < values.size(); i++) {
                    q.offer(values.get(i));
                }
            }

        }

    }

    static class Debug {
        private static final String DEBUG_PROPERTY = "debug";
        private static final String DEBUG_CALL_PATTERN = "^.+\\.debug\\((.+)\\);.*$";
        private static Pattern debugRegex;
        private static boolean enabled = false;
        private static String src;

        public static void enable(String s) {
            enabled = true;
            src = s;
            if (debugRegex == null) {
                debugRegex = Pattern.compile(DEBUG_CALL_PATTERN);
            }
        }

        public static boolean autoEnable() {
            try {
                String s = System.getProperty(DEBUG_PROPERTY);
                if (s != null) {
                    enable(s);
                    return true;
                }
            } catch (AccessControlException ex) {
                src = null;
            }
            return false;
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ans(Object obj) {
            return ans(Objects.toString(obj));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public long longs() {
            return Long.parseLong(string());
        }

    }
}