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:

/*
 * @author romit17
 */

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.PriorityQueue;
import java.util.TreeSet;

public class D1249 {
    
    void solve() throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder("");
        int n = ni(), k = ni();
        points[] a = new points[2*n];
        for(int i=0;i<2*n;i+=2)
        {
            int x = ni(), y = ni();
            a[i] = new points(x, 0, i/2+1);
            a[i+1] = new points(y, 1, i/2+1);
            a[i].y = a[i+1];
            a[i+1].y = a[i];
        }
        
        Arrays.sort(a);
        HashSet<Integer> bad = new HashSet<>();
                
        TreeSet<points> ts = new TreeSet<>((points o1, points o2) -> {
            if(o1.x == o2.x) return o1.id - o2.id;
            return o1.x - o2.x;
        });
        
        for(int i=0;i<2*n;i++)
        {
            if(bad.contains(a[i].id)) continue;
            
            if(a[i].sd == 1)
            {
                ts.remove(a[i]); continue;
            }
            
            ts.add(a[i].y);
            if(ts.size() <= k) continue;
            points lst = ts.last();
            ts.remove(lst);
            bad.add(lst.id);
        }
        out.println(bad.size());
        for(int i:bad) out.print(i+" ");
        out.println();
        out.flush();
    }
    
    class points implements Comparable<points>
    {
        int x;
        points y;
        int sd;
        int id;

        public points(int x, int sd, int id) {
            this.x = x;
            this.y = null;
            this.sd = sd;
            this.id = id;
        }

        @Override
        public int compareTo(points o) {
            if(this.x == o.x)
                return this.sd - o.sd;
            return this.x - o.x;
        }
        
        
    }
    
    
    public static void main(String[] args) throws IOException {
        new D1249().solve();
    }    
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;    
    InputStream is = System.in;

    private int readByte() {
        if (lenbuf == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) {
                return -1;
            }
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
    
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }
    
    private double nd() {
        return Double.parseDouble(ns());
    }
    
    private char nc() {
        return (char) skip();
    }
    
    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) {
            map[i] = ns(m);
        }
        return map;
    }
    
    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }
    
    private int[] na1(int n) {
        int[] a = new int[n + 1];
        for (int i = 1; i < n + 1; i++) {
            a[i] = ni();
        }
        return a;
    }
    
    private long[] nb(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nl();
        }
        return a;
    }
    
    private long[] nb1(int n) {
        long[] a = new long[n + 1];
        for (int i = 1; i < n + 1; i++) {
            a[i] = nl();
        }
        return a;
    }
    
    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
}