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.ArrayList;
import java.util.Scanner;
import java.util.TreeSet;

public class Solution{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();int k = sc.nextInt();
        ArrayList<Pair>[] pairs = new ArrayList[200000+1];
        for(int i=0;i<=200000;i++){
            pairs[i] = new ArrayList<>();
        }

        for(int i=0;i<n;i++){
            int a = sc.nextInt();int b = sc.nextInt();
            Pair p= new Pair(i+1,a,b);
            pairs[a].add(p);
        }


        TreeSet<Pair> treeSet = new TreeSet<>();
        ArrayList<Integer> res = new ArrayList<>();

        for(int i=0;i<=200000;i++){
            while (!treeSet.isEmpty()){
                Pair p = treeSet.last();
                if(p.r < i) treeSet.pollLast();
                else break;
            }
            treeSet.addAll(pairs[i]);
            while (treeSet.size() > k){
                Pair p = treeSet.pollFirst();
                res.add(p.idx);
            }
        }

        StringBuilder sb = new StringBuilder();
        for(int r : res) {sb.append(r + " ");}
        System.out.println(res.size());
        System.out.println(sb.toString().trim());
    }

    private static class Pair implements Comparable<Pair>{
        int idx , l , r;

        public Pair(int idx, int l, int r){
            this.idx = idx;
            this.l = l;
            this.r = r;
        }
        @Override
        public int compareTo(Pair p) {
            if(r == p.r && l == p.l) return idx - p.idx;
            else if(r == p.r) return l - p.l;
            else return p.r - r;
        }
        public String toString() {
            return l+"-"+r;
        }
    }
}