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.util.AbstractQueue;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        D2TooManySegmentsHardVersion solver = new D2TooManySegmentsHardVersion();
        solver.solve(1, in, out);
        out.close();
    }

    static class D2TooManySegmentsHardVersion {
        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            int[] freq = new int[(int) 2e5 + 2];
            ArrayList<Integer>[] add = new ArrayList[(int) 2e5 + 2], remove = new ArrayList[(int) 2e5 + 2];
            for (int i = 0; i < add.length; i++) {
                add[i] = new ArrayList<>();
                remove[i] = new ArrayList<>();
            }
            int[][] pairs = new int[n][2];
            for (int i = 0; i < n; i++) {
                int l = sc.nextInt(), r = sc.nextInt();
                pairs[i][0] = l;
                pairs[i][1] = r;
                freq[l]++;
                freq[r + 1]--;
                add[l].add(i);
                remove[r + 1].add(i);
            }
            for (int i = 1; i < freq.length; i++)
                freq[i] = freq[i - 1] + freq[i];
            PriorityQueue<Integer> pq = new PriorityQueue<>((a, b) -> pairs[b][1] == pairs[a][1] ? pairs[a][0] - pairs[b][0] : pairs[b][1] - pairs[a][1]);
            ArrayList<Integer> ans = new ArrayList<>();
            int sub = 0;
            int[] sub2 = new int[(int) 2e5 + 2];
            boolean[] removed = new boolean[(int) 2e5 + 2];
            for (int i = 0; i <= (int) 2e5; i++) {
                pq.addAll(add[i]);
                for (int x : remove[i])
                    removed[x] = true;
                sub -= sub2[i];
                while (freq[i] - sub > k) {
                    int idx = pq.poll();
                    if (removed[idx])
                        continue;
                    sub2[pairs[idx][1] + 1]++;
                    sub++;
                    ans.add(idx + 1);
                }
            }
            Collections.sort(ans);
            pw.println(ans.size());
            for (int x : ans)
                pw.print(x + " ");
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

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

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

    }
}