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.OutputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Queue;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Rustam Musin (t.me/musin_acm)
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        D2SlishkomMnogoOtrezkovSlozhnayaVersiya solver = new D2SlishkomMnogoOtrezkovSlozhnayaVersiya();
        solver.solve(1, in, out);
        out.close();
    }

    static class D2SlishkomMnogoOtrezkovSlozhnayaVersiya {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int k = in.readInt();
            int maxx = (int) 2e5;
            List<Segment>[] byStart = new List[maxx];
            for (int i = 0; i < maxx; i++) byStart[i] = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                int x = in.readInt() - 1;
                int y = in.readInt() - 1;
                byStart[x].add(new Segment(i, x, y));
            }
            Queue<Segment> q = new PriorityQueue<>();
            Fenwick tree = new Fenwick(maxx);
            List<Segment> ans = new ArrayList<>();
            for (int i = 0; i < maxx; i++) {
                for (Segment s : byStart[i]) {
                    tree.add(s.start, s.end, 1);
                    q.add(s);
                }
                while (tree.get(i) > k) {
                    Segment cur = q.poll();
                    if (cur.end < i) continue;
                    tree.add(cur.start, cur.end, -1);
                    ans.add(cur);
                }
            }
            out.printLine(ans.size());
            for (Segment s : ans) out.print(s.index + 1 + " ");
        }

        class Segment implements Comparable<Segment> {
            int index;
            int start;
            int end;

            public Segment(int index, int start, int end) {
                this.index = index;
                this.start = start;
                this.end = end;
            }

            public int compareTo(Segment o) {
                return -Integer.compare(end, o.end);
            }

        }

        class Fenwick {
            int[] tree;

            Fenwick(int n) {
                tree = new int[n + 1];
            }

            void add(int at, int x) {
                for (at++; at < tree.length; at += at & -at) tree[at] += x;
            }

            void add(int l, int r, int x) {
                add(l, x);
                add(r + 1, -x);
            }

            int get(int at) {
                int s = 0;
                for (at++; at > 0; at -= at & -at) s += tree[at];
                return s;
            }

        }

    }

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

        public InputReader(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 readInt() {
            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 isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void close() {
            writer.close();
        }

        public void printLine(int i) {
            writer.println(i);
        }

    }
}