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.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;
import java.util.TreeSet;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
 
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        APensAndPencils solver = new APensAndPencils();
        solver.solve(1, in, out);
        out.close();
    }
    static class Interval{
    	int x, y;
    	int id;
		public Interval(int x, int y, int id) {
			super();
			this.x = x;
			this.y = y;
			this.id = id;
		}
    }
 
    static class APensAndPencils {
        public void solve(int testNumber, inputClass sc, PrintWriter out) {
            int n=sc.nextInt();
            int k=sc.nextInt();
            Interval[] in=new Interval[n];
            for (int i=0;i<n;i++) {
            	in[i]=new Interval(sc.nextInt(),sc.nextInt(),i);
            }
            Arrays.sort(in, new Comparator<Interval>() {
				@Override
				public int compare(Interval a, Interval b) {
					// TODO Auto-generated method stub
					return Integer.compare(a.x,b.x);
				}
            });
            int[] enter=new int[200001];
            int[] exit=new int[200001];
            for (int i=0;i<n;i++) {
            	enter[in[i].x]++;
            	exit[in[i].y]++;
            }
            int last=0;
            TreeSet<Interval> set=new TreeSet<>(new Comparator<Interval>() {
				@Override
				public int compare(Interval a, Interval b) {
					if (a.y==b.y) {
						return Integer.compare(a.id, b.id);
					}
					return Integer.compare(b.y,a.y);
				}
            });
            ArrayList<Integer> ans=new ArrayList<>();
            int act=0;
            for (int i = 1 ; i<200001;i++) {
            	while (last<n && in[last].x == i) {
            		set.add(in[last]);
            		last++;
            	}
            	act+=enter[i];
            	while (act>k) {
            		Interval tmp=set.pollFirst();
            		ans.add(tmp.id+1);
            		act--;
            		exit[tmp.y]--;
            	}
            	act-=exit[i];
            }
            out.println(ans.size());
            for (int i : ans) {
            	out.print(i+" ");
            }
        }
 
    }
 
    static class inputClass {
        BufferedReader br;
        StringTokenizer st;
 
        public inputClass(InputStream in) {
 
            br = new BufferedReader(new InputStreamReader(in));
        }
 
        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public Long nextLong() {
            return Long.parseLong(next());
        }
 
    }
}