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.util.*;
public class Main
{
    public static class Node implements Comparable<Node>{
        int r;
        int l;
        int i;
        public Node(int x,int y,int z)
        {
            l=x;
            r=y;
            i=z;
        }
        public int compareTo(Node b)
        {
            if(r==b.r)
            {
                if(l==b.l)
                return this.i-b.i;
                return this.l-b.l;
            }
            return r-b.r;
        }
    }
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int ans=0;
		StringBuilder str=new StringBuilder();
		int n=sc.nextInt();
		int k=sc.nextInt();
		ArrayList<Node>[] list=new ArrayList[200001];
		for(int i=0;i<200001;i++)
		list[i]=new ArrayList();
		
		for(int i=0;i<n;i++)
		{
		    int x=sc.nextInt();
		    int y=sc.nextInt();
		    list[x].add(new Node(x,y,i+1));
		}
		TreeSet<Node> set=new TreeSet();
		for(int i=1;i<200001;i++)
		{
		    while(!set.isEmpty())
		    {
		        if(set.first().r<i)
		            set.pollFirst();
		        else
		        break;
		    }
		    set.addAll(list[i]);
		    while(set.size()>k)
		    {
		        str.append(set.pollLast().i+" ");
		        ans++;
		    }
		}
		System.out.println(ans+"\n"+str);
	}
}