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.Arrays;
import java.util.PriorityQueue;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
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;
        FastReader in = new FastReader(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, FastReader s, PrintWriter w) {
            int n = s.nextInt(), k = s.nextInt(), MX = (int) 2e5;
            pair<pair<Integer, Integer>, Integer>[] p = new pair[n];
            bit b = new bit(MX + 1);
            PriorityQueue<pair<Integer, Integer>> pq = new PriorityQueue<>(Collections.reverseOrder());
            for (int i = 1; i <= n; i++) {
                int l = s.nextInt() - 1, r = s.nextInt();
                p[i - 1] = new pair<>(new pair<>(l, r), i);
                b.modify(l, 1);
                b.modify(r, -1);
            }
            ArrayList<Integer> a = new ArrayList<>();
            Arrays.sort(p);
            int cur = 0;
            for (int i = 0; i < MX; i++) {
                while (cur < n && p[cur].x.x == i) {
                    pq.add(new pair<>(p[cur].x.y, p[cur].y));
                    cur++;
                }
                while (b.query(i) > k) {
                    pair<Integer, Integer> pp = pq.poll();
                    b.modify(i, -1);
                    b.modify(pp.x, 1);
                    a.add(pp.y);
                }
            }
            w.println(a.size());
            for (int i : a) w.print(i + " ");
        }

    }

    static class pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<pair<U, V>> {
        public U x;
        public V y;

        public pair(U x, V y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(pair<U, V> other) {
            int i = x.compareTo(other.x);
            if (i != 0) return i;
            return y.compareTo(other.y);
        }

        public String toString() {
            return x.toString() + " " + y.toString();
        }

        public boolean equals(Object obj) {
            if (this.getClass() != obj.getClass()) return false;
            pair<U, V> other = (pair<U, V>) obj;
            return x.equals(other.x) && y.equals(other.y);
        }

        public int hashCode() {
            return 31 * x.hashCode() + y.hashCode();
        }

    }

    static class bit {
        public int n;
        public int[] t;

        public bit(int n) {
            t = new int[n + 1];
            this.n = n;
        }

        public bit(int[] a, int n) {
            t = new int[n + 1];
            this.n = n;
            for (int i = 0; i < n; i++) {
                modify(i, a[i]);
            }
        }

        public void modify(int ind, int val) {
            ind++;
            while (ind <= n) {
                t[ind] += val;
                ind += ind & (-ind);
            }
        }

        public int query(int ind) {
            ind++;
            int sum = 0;
            while (ind > 0) {
                sum += t[ind];
                ind -= ind & (-ind);
            }
            return sum;
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {

            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {

                curChar = 0;

                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }

            return buf[curChar++];
        }

        public int nextInt() {

            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public boolean isSpaceChar(int c) {

            if (filter != null)
                return filter.isSpaceChar(c);

            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}