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.math.BigInteger;
import java.util.*;

public class Solution {

    private static PrintWriter out;

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        MyScanner(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

            return st.nextToken();
        }

        String nextLine() {
            String result = "";

            try {
                result = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return result;
        }

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

        float nextFloat(){
            return Float.parseFloat(next());
        }

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

    public static void main(String[] args) {
        MyScanner scan = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

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

        int N = 200001;

        ArrayList<Segment> segments[] = new ArrayList[N];

        for(int i = 0; i < N; i++){
            segments[i] = new ArrayList<>();
        }

        for(int i = 0; i < n; i++){
            int l = scan.nextInt();
            int r = scan.nextInt();

            segments[l].add(new Segment(l, r, (i+1)));
        }

        ArrayList<Integer> result = new ArrayList<>();
        TreeSet<Segment> trees = new TreeSet<>();
        for(int j = 0; j < N; j++){
            while (!trees.isEmpty()) {
                Segment last = trees.last();
                if(last.r < j) trees.pollLast();
                else break;
            }
            trees.addAll(segments[j]);
            while(trees.size() > k) {
                Segment first = trees.pollFirst();
                result.add(first.index);
            }
        }

        out.println(result.size());
        for(int i = 0; i < result.size(); i++){
            out.print(result.get(i) + " ");
        }

//        for(int j = 0; j < N; j++){
//            trees.addAll(segments[j]);
//        }

//        int len = trees.size();
//        for(int j = 0; j < len; j++){
//            out.println(trees.pollFirst());
//        }

        out.close();
    }

    static class Segment implements Comparable<Segment> {
        int l;
        int r;
        int index;

        Segment(int l, int r, int idx) {
            this.l = l;
            this.r = r;
            index = idx;
        }

        @Override
        public int compareTo(Segment o) {
            if(l == o.l && r == o.r) return index-o.index;
            if(r == o.r) return l-o.l;
            return o.r-r;
//            return -1;
        }

        @Override
        public String toString() {
            return l + " " + r;
        }
    }
}