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.*;
import java.io.*;

public class A
{
    public static void main(String ar[]) throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        
        String s1[]=br.readLine().split(" ");
        int n=Integer.parseInt(s1[0].trim());
        int k=Integer.parseInt(s1[1].trim());
        
        int a[][]=new int[n][3];
        for(int i=0;i<n;i++)
        {
            String s2[]=br.readLine().split(" ");
            int l=Integer.parseInt(s2[0]);
            int r=Integer.parseInt(s2[1]);
            
            a[i][0]=l;
            a[i][1]=r;
            a[i][2]=i;
        }
        
        Arrays.sort(a,new Comparator<int []>(){
            public int compare(final int a1[],final int a2[])
            {
                if(a1[0]>a2[0])
                 return 1;
                else if(a1[0]==a2[0])
                 return 0;
                else
                 return -1;
            }
        });
        
        int b[][]=new int[n][3];
        for(int i=0;i<n;i++)
        {
            b[i][0]=a[i][0];
            b[i][1]=a[i][1];
            b[i][2]=i;
        }
        
        Arrays.sort(b,new Comparator<int []>(){
            public int compare(final int a1[],final int a2[])
            {
                if(a1[1]>a2[1])
                 return 1;
                else if(a1[1]==a2[1])
                 return 0;
                else
                 return -1;
            }
        });
        
        // for(int i=0;i<n;i++)
        //  System.out.println(a[i][0]+" "+a[i][1]+" "+a[i][2]);
         
        // System.out.println();
        
        // for(int i=0;i<n;i++)
        //  System.out.println(a[i][0]+" "+a[i][1]+" "+a[i][2]);
        
        int j=0;
        int h=0;
        int count=0;
        
        int w=0;
        StringBuffer sb=new StringBuffer();
        
        TreeMap<Integer,Queue<Integer>> tm=new TreeMap<>();
        HashSet<Integer> hs=new HashSet<Integer>();
        for(int i=0;i<=200000;i++)
        {
            while(j<n && a[j][0]<=i)
            { 
                hs.add(j);
                if(!tm.containsKey(a[j][1]))
                { 
                    Queue<Integer> al=new LinkedList<Integer>();
                    al.add(j);
                    tm.put(a[j][1],al); 
                }
                else
                    tm.get(a[j][1]).add(j);
                j++; count++; 
            }
            
            // if(i==28 || i==29 || i==30)
            // System.out.println("hashmap "+i+" "+hs+" "+h);
            
            while(h<n && b[h][1]<i)
            { 
                if(hs.contains(b[h][2]))
                { hs.remove(b[h][2]); count--; }
                h++;
            }
            
            // if(i==28 || i==29 || i==30)
            // System.out.println(i+" "+tm);
            
            if(count<=k)
             continue;
            
            while(count>k)
            {
                int v=tm.lastKey();
                // System.out.println(i+" "+v);
                if(tm.get(v).size()>1)
                {
                    int z=tm.get(v).poll();
                    hs.remove(z);
                    count--;
                    w++;
                    sb.append(a[z][2]+1).append(" ");
                }
                else
                {
                    int z=tm.get(v).poll();
                    hs.remove(z);
                    count--;
                    tm.remove(v);
                    w++;
                    sb.append(a[z][2]+1).append(" ");
                }
            }
        }
        
        System.out.println(w);
        System.out.println(sb);
    }
}