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.util.*;

public class E1066 {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();

    }

    static class InputReader {
        StringTokenizer tokenizer;
        InputStreamReader sReader;
        BufferedReader reader;

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

        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());
        }

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

        public List<Integer> intLine(int size) {
            List<Integer> ls = new ArrayList<>(size);
            for (int i = 0; i < size; i++) {
                ls.add(nextInt());
            }
            return ls;
        }

        int nextC() {
            try {
                return reader.read();
            } catch (IOException e) {
                return -1;
            }
        }

        public int[] intArr(int size) {
            int[] ls = new int[size];
            for (int i = 0; i < size; i++) ls[i] = nextInt();
            return ls;
        }
    }

    public static class Solver {
        private void solve(InputReader inp, PrintWriter out) {
            int n=inp.nextInt(),k=inp.nextInt(), removed=0;
            boolean[] rm= new boolean[n];
            ArrayList<Obj> starts = new ArrayList<>(n+1), ends= new ArrayList<>(n+1);
            Obj[] endarr = new Obj[n];
            for (int i=0;i<n;i++){
                int a =inp.nextInt(),b=inp.nextInt();
                starts.add(new Obj(a,i));
                endarr[i]=new Obj(b,i);
                ends.add(endarr[i]);
            }
            Collections.sort(starts,Comparator.reverseOrder());
            Collections.sort(ends,Comparator.reverseOrder());
            PriorityQueue<Obj> pq = new PriorityQueue<>();
            int cv=0;
            ListIterator<Obj> sli = starts.listIterator(),eli = ends.listIterator();
            Obj curr = sli.next();
            Obj end = eli.next();
            while (true){
                while (curr.a >end.a){
                    if (!rm[end.nr]) cv--;
                    end=eli.next();
                }
                pq.add(endarr[curr.nr]);

                if (cv == k){
                    Obj val = pq.poll();
                    rm[val.nr]=true;
                    removed++;
                } else {
                    cv++;
                }
                if (!sli.hasNext()) break;
                curr=sli.next();
            }
            out.println(removed);
            for (int i=0;i<n;i++){
                if (rm[i]) out.print(i+1+" ");
            }

        }
    }

    private static class Obj implements Comparable<Obj> {
        int a,nr;

        public Obj(int a, int nr){
            this.a=a;this.nr=nr;
        }

        @Override
        public String toString() {
            return "("+ a +": "+nr+")";
        }

        @Override
        public int compareTo(Obj o) {
            return -Integer.compare(a, o.a);
        }
    }

}