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 javafx.util.Pair;

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

public class Solve1 {

    public static void main(String[] args) {
        PrintWriter pw = new PrintWriter(System.out);
        new Solve1().solve(pw);
        pw.flush();
        pw.close();
    }

    public void solve(PrintWriter pw) {
        FastReader sc = new FastReader();
        int n = sc.nextInt(), k = sc.nextInt();
        Query[] seg = new Query[n];
        for (int i = 0; i < n; i++) {
            seg[i] = new Query(sc.nextInt(), sc.nextInt(), i+1);
        }
        Comparator<Query> cmp = new Comparator<Query>() {
            @Override
            public int compare(Query p1, Query p2) {
                if (p1.l == p2.l) {
                    return p1.r - p2.r;
                }
                return p1.l - p2.l;
            }
        };
        Arrays.sort(seg, cmp);
        final int MAX = (int) 2E+5;
        ArrayList<Integer> ans = new ArrayList<>();
        TreeMap<Integer, ArrayList<Integer>> tm = new TreeMap<>();
        int size = 0;
        for (int l = 1, j = 0; l <= MAX; l++) {
            while (j < n && l == seg[j].l) {
                tm.putIfAbsent(seg[j].r, new ArrayList());
                tm.get(seg[j].r).add(seg[j].ind);
                ++size;
                if (size > k) {
                    ArrayList<Integer> temp = tm.lastEntry().getValue();
                    ans.add(temp.get(temp.size() - 1));
                    temp.remove(temp.size() - 1);
                    if (temp.isEmpty()) tm.pollLastEntry();
                    --size;
                }
                ++j;
            }
            if (!tm.isEmpty() && l == tm.firstKey()) {
                size-=tm.firstEntry().getValue().size();
                tm.pollFirstEntry();
            }
        }
        pw.println(ans.size());
        for (int i = 0; i < ans.size(); i++) {
            pw.print((i == 0 ? "" : " ") + ans.get(i));
        }
        pw.println();
    }

    static class Query {
        int l, r, ind;

        public Query(int l, int r, int ind) {
            this.l = l;
            this.r = r;
            this.ind = ind;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
            }
        }

        public String next() {
            if (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean hasNext() throws IOException {
            if (st != null && st.hasMoreTokens()) return true;
            String s = br.readLine();
            if (s == null || s.isEmpty()) return false;
            st = new StringTokenizer(s);
            return true;
        }
    }
}