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 Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            int k=input.nextInt();
            Pair arr[]=new Pair[n+1];
            for(int i=1;i<=n;i++)
            {
                int l=input.nextInt();
                int r=input.nextInt();
                arr[i]=new Pair(l,r,i);
            }
            mergeSort(arr,1,n);
            HashSet<Integer> adj[]=new HashSet[200002];
            for(int i=1;i<adj.length;i++)
            {
                adj[i]=new HashSet<>();
            }
            for(int i=1;i<=n;i++)
            {
                int l=arr[i].l;
                int r=arr[i].r;
                adj[l].add(i);
                adj[r+1].add(-i);
            }
            TreeSet<Integer> set=new TreeSet<>();
            ArrayList<Integer> list=new ArrayList<>();
            for(int i=1;i<adj.length;i++)
            {
                Iterator it=adj[i].iterator();
                while(it.hasNext())
                {
                    int v=(int)it.next();
                    if(v>0)
                    {
                        set.add(v);
                    }
                    else
                    {
                        set.remove(-v);
                    }
                }
                if(set.size()>k)
                {
                    while(set.size()>k)
                    {
                        int v=set.pollLast();
                        int r=arr[v].r;
                        adj[r+1].remove(-v);
                        list.add(v);
                    }
                }
            }
            out.println(list.size());
            for(int i=0;i<list.size();i++)
            {
                int v=list.get(i);
                out.print(arr[v].index+" ");
            }
            out.println();
        }
        out.close();
    }
    public static void mergeSort(Pair a[],int p,int r)
    {
        if(p<r)
        {
            int q=(p+r)/2;
            mergeSort(a,p,q);
            mergeSort(a,q+1,r);
            merge(a,p,q,r);
        }
    }
    public static void merge(Pair a[],int p,int q,int r)
    {
        int n1=q-p+2;
        Pair L[]=new Pair[n1];
        int n2=r-q+1;
        Pair R[]=new Pair[n2];
        for(int i=p;i<=q;i++)
        {
            L[i-p]=a[i];
        }
        L[n1-1]=new Pair(0,Integer.MAX_VALUE,0);
        for(int i=q+1;i<=r;i++)
        {
            R[i-q-1]=a[i];
        }
        R[n2-1]=new Pair(0,Integer.MAX_VALUE,0);
        int x=0,y=0;
        for(int i=p;i<=r;i++)
        {
            if(L[x].r<=R[y].r)
            {
                a[i]=L[x];
                x++;
            }
            else
            {
                a[i]=R[y];
                y++;
            }
        }
    }
    static class Pair
    {
        int l,r,index;
        Pair(int l,int r,int index)
        {
            this.l=l;
            this.r=r;
            this.index=index;
        }
    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt()
        {
            return Integer.parseInt(next());
        }
        long nextLong()
        {
            return Long.parseLong(next());
        }
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}