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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jaynil
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD2 solver = new TaskD2();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD2 {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            ArrayList<int[]> ll = new ArrayList<>();
            ArrayList<int[]> rr = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                ll.add(new int[]{in.nextInt(), in.nextInt(), i});
            }
            Collections.sort(ll, (x, y) -> x[0] - y[0]);
            int l = 0;
            int r = 0;
            PriorityQueue<int[]> pq = new PriorityQueue<>((x, y) -> y[0] - x[0]);
            PriorityQueue<int[]> q = new PriorityQueue<>((x, y) -> x[0] - y[0]);
            int count = 0;
            HashSet<Integer> ans = new HashSet<>();
            int j = 0;
            for (int i = 1; i <= 200000; i++) {
                while (j < n && ll.get(j)[0] <= i) {
                    pq.add(new int[]{ll.get(j)[1], ll.get(j)[2]});
                    q.add(new int[]{ll.get(j)[1], ll.get(j)[2]});
                    j++;
                    count++;
                }

                while (q.size() > 0 && q.peek()[0] < i) {
                    int temp[] = q.poll();
                    if (!ans.contains(temp[1])) {
                        count--;
                    }
                }
                while (count > k) {
                    int temp[] = pq.poll();
                    ans.add(temp[1]);
                    count--;
                }
            }
//        out.println(count);
            out.println(ans.size());
            for (int x : ans) out.print((x + 1) + " ");
            out.println();
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}