Problem: The only difference between easy and hard versions is constraints.

You are given n segments on the coordinate axis OX. Segments can intersect, lie inside each other and even coincide. The i-th segment is [l_i; r_i] (l_i ≤ r_i) and it covers all integer points j such that l_i ≤ j ≤ r_i.

The integer point is called bad if it is covered by strictly more than k segments.

Your task is to remove the minimum number of segments so that there are no bad points at all.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of segments and the maximum number of segments by which each integer point can be covered.

The next n lines contain segments. The i-th line contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ 2 ⋅ 10^5) — the endpoints of the i-th segment.

Output

In the first line print one integer m (0 ≤ m ≤ n) — the minimum number of segments you need to remove so that there are no bad points.

In the second line print m distinct integers p_1, p_2, ..., p_m (1 ≤ p_i ≤ n) — indices of segments you remove in any order. If there are multiple answers, you can print any of them.

Examples

Input


7 2
11 11
9 11
7 8
8 9
7 8
9 11
7 9


Output


3
4 6 7 


Input


5 1
29 30
30 30
29 29
28 30
30 30


Output


3
1 4 5 


Input


6 1
2 3
3 3
2 3
2 2
2 3
2 3


Output


4
1 3 5 6 

Solution (in JAVA):

Solution:
import java.io.*;
import java.nio.CharBuffer;
import java.util.*;

public class P1249D_2 {

    private static final int MAX = 200_000;

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int n = scanner.nextInt();
        int k = scanner.nextInt();
        HashMap<Integer, List<Integer>> s = new HashMap<>();
        HashMap<Integer, List<Integer>> e = new HashMap<>();
        int[] l = new int[n];
        int[] r = new int[n];
        for (int i = 0; i < n; ++i) {
            l[i] = scanner.nextInt();
            r[i] = scanner.nextInt();
            s.putIfAbsent(l[i], new ArrayList<>());
            s.get(l[i]).add(i);
            e.putIfAbsent(r[i], new ArrayList<>());
            e.get(r[i]).add(i);
        }
        TreeMap<Integer, List<Integer>> rMap = new TreeMap<>();
        LinkedList<Integer> ans = new LinkedList<>();
        for (int i = 1, size = 0; i <= MAX; ++i) {
            if (s.get(i) != null)
                for (int idx : s.get(i)) {
                    rMap.putIfAbsent(r[idx], new ArrayList<>());
                    rMap.get(r[idx]).add(idx);
                    ++size;
                }
            while (size > k) {
                Map.Entry<Integer, List<Integer>> entry = rMap.pollLastEntry();
                int key = entry.getKey();
                List<Integer> list = entry.getValue();
                if (size - list.size() < k) {
                    for (int j = 0; j < size - k; ++j)
                        ans.add(list.get(j));
                    ArrayList<Integer> newList = new ArrayList<>(list.size());
                    for (int j = size - k; j < list.size(); ++j)
                        newList.add(list.get(j));
                    size = k;
                    rMap.put(key, newList);
                } else {
                    ans.addAll(list);
                    size -= list.size();
                }
            }
            List<Integer> end = rMap.remove(i);
            if (end != null)
                size -= end.size();
        }
        writer.println(ans.size());
        for (int v : ans)
            writer.print(v + 1 + " ");


        writer.close();
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        private SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        private void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        private char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        private String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

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

        private long nextLong() {
            return Long.parseLong(next());
        }

        private double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}