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.lang.*;
import java.util.*;

public class D2_1249 {
    static int[] segtree;
    public static void main(String[] args) throws IOException{
        StringBuffer ans = new StringBuffer();
        StringTokenizer st;
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        int[] arr1 = new int[2*(int)Math.pow(10,5) + 2];
        point[] arr = new point[n];
        ArrayList<Integer>[] use = new ArrayList[arr1.length];
        for(int i = 0; i < n; i++){
            st = new StringTokenizer(f.readLine());
            int ft = Integer.parseInt(st.nextToken()) - 1;
            int sc = Integer.parseInt(st.nextToken()) - 1;
            arr1[ft]++;
            arr1[sc+1]--;
            arr[i] = new point(sc, ft, i+1);
            if(use[sc+1] == null)
                use[sc+1] = new ArrayList<>();
            if(use[ft] == null)
                use[ft] = new ArrayList<>();
            use[ft].add(i+1);
            use[sc+1].add(-(i+1));
        }
        f.close();
        int[] psums = new int[arr1.length];
        for(int i = 0; i < arr1.length; i++){
            if(i != 0)
                psums[i] = psums[i-1];
            psums[i]+=arr1[i];
        }


        int[] add = new int[arr1.length];
        int sub = 0;
        ArrayList<Integer> arrl = new ArrayList<>();
        PriorityQueue<point> pq = new PriorityQueue<>(Collections.reverseOrder());
        boolean[] visited = new boolean[n];
        for(int i = 0; i < arr1.length; i++){
            sub+=add[i];
            if(use[i] != null){
                for(int x : use[i]){
                    if(x < 0)
                        visited[-x-1] = true;
                    else
                        pq.add(arr[x-1]);
                }
            }
            if(psums[i] - sub <= k) continue;
            while (psums[i] - sub > k){
                if(visited[pq.peek().index-1]){
                    pq.poll();
                    continue;
                }
                sub++;
                arrl.add(pq.peek().index);
                add[pq.poll().x+1]--;
            }
        }

        ans.append(arrl.size()).append("\n");
        for(int i : arrl)
            ans.append(i).append(" ");



        System.out.println(ans);
    }
    public static class point implements Comparable<point>{
        int x;
        int y;
        int index;
        public point(int x,int y, int index){
            this.x = x;
            this.y = y;
            this.index = index;
        }
        public String toString(){
            return(x + " " + y);
        }
        public int compareTo(point other){
            if(this.x > other.x || (this.x == other.x && this.y < other.y)){
                return 1;
            }else if(this.x == other.x && other.y == this.y){
                return 0;
            }
            return -1;
        }
    }

}