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:
//When I wrote this code, only God & I understood what it did. Now only God knows !!

import java.util.*;
import java.io.*;
import java.math.*;
public class Main {

    static class FastReader
    {
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public FastReader() { this(System.in); }public FastReader(InputStream is) { mIs = is;}
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];}
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;}
        public String next(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();}
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;}
        public int i(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;}
        public double d() throws IOException {return Double.parseDouble(next()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
        public void scanIntArr(int [] arr){ for(int li=0;li<arr.length;++li){ arr[li]=i();}}
        public void scanLongArr(long [] arr){for (int i=0;i<arr.length;++i){arr[i]=l();}}
        public void shuffle(int [] arr){ for(int i=arr.length;i>0;--i) { int r=(int)(Math.random()*i); int temp=arr[i-1]; arr[i-1]=arr[r]; arr[r]=temp; } }
    }

    public static int mod = (int) (1e9 + 7);

    public static void main(String[] args) throws IOException {
        // new Thread(null,new Main(),"Anything",1<<27).start();

        FastReader fr = new FastReader();
        PrintWriter pw = new PrintWriter(System.out);
        /*
inputCopy
7 2
11 11
9 11
7 8
8 9
7 8
9 11
7 9
outputCopy
3
4 6 7
inputCopy
5 1
29 30
30 30
29 29
28 30
30 30
outputCopy
3
1 4 5
inputCopy
6 1
2 3
3 3
2 3
2 2
2 3
2 3
outputCopy
4
1 3 5 6
        */

        int n=fr.i();
        int k=fr.i();
        boolean [] used=new boolean[n+1];
        PriorityQueue<Segment> pq=new PriorityQueue<>();
        for(int i=0;i<n;++i)
        {
            int li=fr.i();
            int ri=fr.i();
            Segment start=new Segment(li,ri+1,i+1,true,li);
            Segment end=new Segment(li,ri+1,i+1,false,ri+1);
            pq.add(start);
            pq.add(end);
        }
        int curLoad=0;
        HashSet<Integer> ans=new HashSet<>();
        PriorityQueue<Segment> curSegments=new PriorityQueue<>(new Comparator<Segment>() {
            @Override
            public int compare(Segment segment, Segment t1) {
                return Integer.compare(segment.r,t1.r)*-1;
            }
        });
        while(!pq.isEmpty())
        {
            Segment segment=pq.remove();
            //System.err.println("Segment: " +segment);
            if(segment.start)
            {
                curSegments.add(segment);
                ++curLoad;
                if(curLoad>k)
                {
                    Segment removedSegment=curSegments.remove();
                    //System.err.println("Removed: "+removedSegment.index);
                    ans.add(removedSegment.index);
                    used[removedSegment.index]=true;
                    --curLoad;
                }
            }
            else
            {
                if(!used[segment.index])
                {
                    --curLoad;
                }
            }
            //System.err.println("Load: "+curLoad);
            //System.err.println(Arrays.toString(used));
        }
        pw.println(ans.size());
        for(int num:ans)
            pw.print(num+" ");
        pw.flush();
        pw.close();
    }
    static class Segment implements Comparable<Segment>
    {
        int l,r,index;
        int point;
        boolean start;

        public Segment(int l, int r, int index,boolean start,int point) {
            this.l = l;
            this.r = r;
            this.index = index;
            this.start=start;
            this.point=point;
        }

        @Override
        public int compareTo(Main.Segment other) {
            if(this.point!=other.point)
                return Integer.compare(this.point,other.point);
            if(this.start==false)
                return -1;
            if(other.start==false)
                return 1;
            return Integer.compare(this.r,other.r);
        }
        public String toString()
        {
            return this.start+" "+this.index+" "+this.l+" "+(this.r-1)+" "+this.point;
        }
    }
}