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:
//package codeforces.round595div3;

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

public class TooManySegmentsHard {
    private static class Segment {
        int l, r, idx;
        Segment(int l, int r, int idx) {
            this.l = l;
            this.r = r;
            this.idx = idx;
        }

        int getL() {
            return l;
        }

        int getR() {
            return r;
        }

        int getIdx() { return idx; }
    }
    public static void main(String[] args) {
//        try {
//            FastScanner in = new FastScanner(new FileInputStream("src/input.in"));
//            PrintWriter out = new PrintWriter(new FileOutputStream("src/output.out"));
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int k = in.nextInt();

        int[] cnt = new int[(int)2e5 + 1];
        Segment[] s = new Segment[n];
        for(int i = 0; i < n; i++) {
            s[i] = new Segment(in.nextInt() - 1, in.nextInt() - 1, i);
        }
        Arrays.sort(s, Comparator.comparingInt(Segment::getL));

        PriorityQueue<Segment> q = new PriorityQueue<>(Comparator.comparingInt(Segment::getR).reversed());

        int ptr = 0, add = 0;
        //Set<Integer> indices = new HashSet<>();
        List<Integer> indices = new ArrayList<>();
        for(int i = 0; i < (int) 2e5; i++) {
                while (ptr < n && s[ptr].l <= i) {
                    q.add(s[ptr]);
                    cnt[s[ptr].r + 1]--;
                    ptr++;
                    add++;
                }
                add += cnt[i];
                while (add > k) {
                    Segment curS = q.poll();
                    indices.add(curS.getIdx());
                    add--;
                    cnt[curS.r + 1]++;
                }
        }

        out.println(indices.size());
        for (int i : indices) {
            out.print((i + 1) + " ");
        }
        out.close();

//        }
//        catch (IOException e) {
//            e.printStackTrace();
//        }
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}