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:
//package main;

import java.io.*;
import java.util.*;

public final class Main {
    BufferedReader br;
    StringTokenizer stk;
    
    public static void main(String[] args) throws Exception {
        new Main().run();
    }
    
    {
        stk = null;
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    
    long mod = 998244353;
    StringBuilder res = new StringBuilder(1000005);
    void run() throws Exception {
        int n = ni(), k = ni();
        List<Segment>[] lists = new ArrayList[200005];
        for(int i = 0; i < lists.length; i++) {
            lists[i] = new ArrayList<>();
        }
        for(int i = 0; i < n; i++) {
            Segment s = new Segment(i + 1, ni(), ni());
            lists[s.left].add(s);
        }
        
        // Using TreeSet as a double-ended PQueue
        // Since it has function to remove Min as well as Max
        // No equals and hashcode methods are overriden
        // So that multiple copies of the same elements may continue to exist in one TreeSet
        TreeSet<Segment> pqueue = new TreeSet<>();
        List<Integer> removed = new ArrayList<>();
        for(int i = 0; i < lists.length; i++) {
            while(!pqueue.isEmpty()) {
                if(pqueue.first().right < i) {
                    pqueue.pollFirst();
                } else {
                    break;
                }
            }
            pqueue.addAll(lists[i]);
            while(pqueue.size() > k) {
                removed.add(pqueue.pollLast().idx);
            }
        }
        
        res.append(removed.size()).append("\n");
        for(int idx : removed) {
            res.append(idx).append(" ");
        }
        System.out.println(res.deleteCharAt(res.length() - 1));
    }
    
    class Segment implements Comparable<Segment> {
        int idx, left, right;
        public Segment(int idx, int left, int right) {
            this.left  = left;
            this.right = right;
            this.idx   = idx;
        }
        @Override
        public int compareTo(Segment seg) {
            if(this.right == seg.right) {
                if(this.left == seg.left) {
                    return this.idx - seg.idx;
                } else {
                    return this.left - seg.left;
                }
            } else {
                return this.right - seg.right;
            }
        }
        @Override
        public String toString() {
            return "[" + this.left + ", " + this.right + "]";
        }
    }
    
    //Reader & Writer
    String nextToken() throws Exception {
        if (stk == null || !stk.hasMoreTokens())
            stk = new StringTokenizer(br.readLine(), " ");
        return stk.nextToken();
    }

    String nt() throws Exception {
        return nextToken();
    }

    int ni() throws Exception {
        return Integer.parseInt(nextToken());
    }

    long nl() throws Exception {
        return Long.parseLong(nextToken());
    }
    
    double nd() throws Exception {
        return Double.parseDouble(nextToken());
    }
    
    //Some Misc methods
    int get(int l, int r, int[] a) {
        return l == 0 ? a[r] : a[r] - a[l - 1];
    }
    
    void shuffle(int[] a) {
        Random r = new Random();
        for(int i = 0; i < a.length; i++) {
            int idx = r.nextInt(a.length);
            int temp = a[i];
            a[i] = a[idx];
            a[idx] = temp;
        }
    }
}