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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

import java.util.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Comparator<int[]> comparator = new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return Integer.compare(o2[0], o1[0]);
            }
        };
        Comparator<int[]> comparator_2 = new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return Integer.compare(o1[0], o2[0]);
            }
        };

        int n = in.nextInt();
        int k = in.nextInt();
        ArrayList<PriorityQueue<int[]>> list = new ArrayList<PriorityQueue<int[]>>();
        for (int i=0;i<200000;i++) { // tmp length
            PriorityQueue<int[]> add = new PriorityQueue<int[]>(comparator);
            list.add(add);
        }
        // int[0] = r-1 int[1] = edge_num;
        long[] height = new long[200000]; // tmp length
        PriorityQueue<Integer> l_pq = new PriorityQueue<Integer>();
        PriorityQueue<int[]> r_pq = new PriorityQueue<int[]>(comparator_2); // int[0]=r int[1]=index
        int l_min = 0;
        int r_max = 0;
        for (int i=0;i<n;i++) {
            int l = in.nextInt()-1;
            int r = in.nextInt()-1;
            l_min = Math.min(l_min, l);
            r_max = Math.max(r_max, r);
            // for (int kk=l;kk<=r;kk++) {
            //     height[kk]++;
            // }
            int[] add = {r, i};
            list.get(l).add(add);

            l_pq.add(l);
            r_pq.add(add);
        }

        long tmp_height = 0;
        int cnt = 0;
        int[] used = new int[n];
        ArrayList<Integer> ans = new ArrayList<Integer>();
        PriorityQueue<int[]> queue_all = new PriorityQueue<int[]>(comparator);
        for (int i=l_min;i<=r_max;i++) {
            if (!l_pq.isEmpty()) {
                while(l_pq.peek()==i) {
                    tmp_height++;
                    l_pq.poll();
                    if (l_pq.isEmpty()) {
                        break;
                    }
                }
            }
            if (!r_pq.isEmpty()) {
                while(r_pq.peek()[0]+1==i) {
                    int[] rem = r_pq.poll();
                    if (used[rem[1]]==0) {
                        tmp_height--;
                    }
                    if (r_pq.isEmpty()) {
                        break;
                    }
                }
            }
            PriorityQueue<int[]> queue = list.get(i);
            queue_all.addAll(queue);
            // while(height[i]>k) {
            // out.println("i: " + i + " tmp_height: " + tmp_height);
            while(tmp_height>k) {
                int[] rem = queue_all.poll();
                // out.print(rem[1] + " ");
                ans.add(rem[1]+1);
                used[rem[1]]=1;
                cnt++;

                tmp_height--;
                // for (int j=i;j<=rem[0];j++) {
                //     height[j]--;
                // }
            }
            // out.println("i: " + i + " tmp_height: " + tmp_height);
        }
        out.println(cnt);
        for (int i=0;i<ans.size();i++) {
            if (i==ans.size()-1) {
                out.println(ans.get(i));
            } else {
                out.print(ans.get(i) + " ");
            }
        }
        // System.out.println(list);

        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

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

    }
}