Problem: Easy and hard versions are actually different problems, so read statements of both problems completely and carefully.

Summer vacation has started so Alice and Bob want to play and joy, but... Their mom doesn't think so. She says that they have to read exactly m books before all entertainments. Alice and Bob will read each book together to end this exercise faster.

There are n books in the family library. The i-th book is described by three integers: t_i — the amount of time Alice and Bob need to spend to read it, a_i (equals 1 if Alice likes the i-th book and 0 if not), and b_i (equals 1 if Bob likes the i-th book and 0 if not).

So they need to choose exactly m books from the given n books in such a way that:

  * Alice likes at least k books from the chosen set and Bob likes at least k books from the chosen set; 
  * the total reading time of these m books is minimized (they are children and want to play and joy as soon a possible). 



The set they choose is the same for both Alice an Bob (it's shared between them) and they read all books together, so the total reading time is the sum of t_i over all books that are in the chosen set.

Your task is to help them and find any suitable set of books or determine that it is impossible to find such a set.

Input

The first line of the input contains three integers n, m and k (1 ≤ k ≤ m ≤ n ≤ 2 ⋅ 10^5).

The next n lines contain descriptions of books, one description per line: the i-th line contains three integers t_i, a_i and b_i (1 ≤ t_i ≤ 10^4, 0 ≤ a_i, b_i ≤ 1), where:

  * t_i — the amount of time required for reading the i-th book; 
  * a_i equals 1 if Alice likes the i-th book and 0 otherwise; 
  * b_i equals 1 if Bob likes the i-th book and 0 otherwise. 

Output

If there is no solution, print only one integer -1.

If the solution exists, print T in the first line — the minimum total reading time of the suitable set of books. In the second line print m distinct integers from 1 to n in any order — indices of books which are in the set you found.

If there are several answers, print any of them.

Examples

Input

6 3 1
6 0 0
11 1 0
9 0 1
21 1 1
10 1 0
8 0 1


Output

24
6 5 1 

Input

6 3 2
6 0 0
11 1 0
9 0 1
21 1 1
10 1 0
8 0 1


Output

39
4 6 5 

Solution (in JAVA):

Solution:
//package div3._1374;

import java.io.*;
import java.util.*;

public class ReadingBooksHardVersion {

    private final FastReader fr = new FastReader();

    public static void main(String[] args) {
        new ReadingBooksHardVersion().solve();
    }

    private void solve() {
        final int n = fr.nextInt(), m = fr.nextInt(), k = fr.nextInt();

        List<Book> groupA = new ArrayList<>(),
                groupB = new ArrayList<>(),
                groupAB = new ArrayList<>(),
                groupNotAB = new ArrayList<>();

        for (int index = 0; index < n; index++) {
            int time = fr.nextInt(), a = fr.nextInt(), b = fr.nextInt();
            Book book = new Book(index + 1, time);
            if (a == 1 && b == 1) groupAB.add(book);
            else if (a == 1) groupA.add(book);
            else if (b == 1) groupB.add(book);
            else groupNotAB.add(book);
        }

        Collections.sort(groupA);
        Collections.sort(groupB);
        Collections.sort(groupAB);
        Collections.sort(groupNotAB);

        Set<Book> books = readingBooks(groupNotAB, groupA, groupB, groupAB, m, k);
        printAns(books);

    }

    private void printAns(Set<Book> books) {
        if (books == null)
            System.out.println(-1);
        else {
            int time = 0;
            StringBuilder s = new StringBuilder();
            for (Book b : books) {
                time += b.time;
                s.append(b.index).append(" ");
            }
            System.out.printf("%d\n%s\n", time, s);
        }
    }


    private Set<Book> readingBooks(List<Book> groupNotAB,
                                   List<Book> groupA,
                                   List<Book> groupB,
                                   List<Book> groupAB,
                                   int m,
                                   int k) {

        int ai = 0; // group A index
        int bi = 0; // group B index
        int abi = 0; // group AB index
        int noni = 0; // group not AB index

        Set<Book> books = new HashSet<>();
        for (int i = 1; i <= k; i++) {
            Integer both = (groupAB.size() > abi) ? groupAB.get(abi).time : null;
            Integer separate = (groupA.size() > ai && groupB.size() > bi) ? groupA.get(ai).time + groupB.get(bi).time : null;

            if (both == null && separate == null) return null;

            if (beats(both, separate)) {
                books.add(groupAB.get(abi++));
            } else {
                books.add(groupA.get(ai++));
                books.add(groupB.get(bi++));
            }
        }

        int booksDiff = Math.abs(m - books.size()); // books difference

        if (m < books.size()) {
            // remove books
            for (int i = 1; i <= booksDiff; i++) {
                if (ai == 0 || bi == 0 || groupAB.size() <= abi) return null;
                books.remove(groupA.get(--ai));
                books.remove(groupB.get(--bi));
                books.add(groupAB.get(abi++));
            }
        } else {
            // add more books
            for (int i = 1; i <= booksDiff; i++) {
                Action swap = new Action(
                        "swap",
                        (groupA.size() > ai && groupB.size() > bi && abi > 0)
                                ? groupA.get(ai).time + groupB.get(bi).time - groupAB.get(abi - 1).time
                                : null
                );
                Action addNone = new Action(
                        "addNone",
                        (groupNotAB.size() > noni)
                                ? groupNotAB.get(noni).time
                                : null
                );
                Action addA = new Action(
                        "addA",
                        (groupA.size() > ai)
                                ? groupA.get(ai).time
                                : null
                );
                Action addB = new Action(
                        "addB",
                        (groupB.size() > bi)
                                ? groupB.get(bi).time
                                : null
                );
                Action addBoth = new Action(
                        "addBoth",
                        (groupAB.size() > abi)
                                ? groupAB.get(abi).time
                                : null
                );

                String action = findTheBestAction(new ArrayList<Action>() {{
                    add(swap);
                    add(addNone);
                    add(addA);
                    add(addB);
                    add(addBoth);
                }});

                switch (action) {
                    case "null":
                        return null;
                    case "swap":
                        books.remove(groupAB.get(--abi));
                        books.add(groupA.get(ai++));
                        books.add(groupB.get(bi++));
                        break;
                    case "addNone":
                        books.add(groupNotAB.get(noni++));
                        break;
                    case "addA":
                        books.add(groupA.get(ai++));
                        break;
                    case "addB":
                        books.add(groupB.get(bi++));
                        break;
                    case "addBoth":
                        books.add(groupAB.get(abi++));
                        break;
                }

            }

        }

        return books;
    }

    private String findTheBestAction(ArrayList<Action> integers) {
        Optional<Action> min = integers.stream().filter(item -> item.value != null).min(Comparator.comparingInt(a -> a.value));
        return min.map(action -> action.name).orElse("null");
    }


    private boolean beats(Integer a, Integer b) {
        return b == null || (a != null && a < b);
    }

    static class Action {
        @Override
        public String toString() {
            return "Action{" +
                    "name='" + name + '\'' +
                    ", value=" + value +
                    '}';
        }

        private final String name;
        private final Integer value;

        public Action(String name, Integer value) {
            this.name = name;
            this.value = value;
        }
    }

    static class Book implements Comparable<Book> {

        private final int index;
        private final int time;

        public Book(int index, int time) {
            this.index = index;
            this.time = time;
        }

        @Override
        public String toString() {
            return "Book{" +
                    "index=" + index +
                    ", time=" + time +
                    '}';
        }

        @Override
        public int compareTo(Book o) {
            return this.time - o.time;
        }
    }

    static class FastReader {
        private final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private StringTokenizer st;

        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException ex) {
                throw new RuntimeException(ex);
            }
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
    }

}