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.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.TreeMap;
import java.util.Map;
import java.util.Map.Entry;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Mufaddal Naya
 */
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);
        D1TooManySegmentsEasyVersion solver = new D1TooManySegmentsEasyVersion();
        solver.solve(1, in, out);
        out.close();
    }

    static class D1TooManySegmentsEasyVersion {
        public void solve(int testNumber, InputReader c, OutputWriter w) {
            int n = c.readInt(), k = c.readInt();
            Points[] seg = new Points[n];
            for (int i = 0; i < n; ++i) {
                int u = c.readInt(), v = c.readInt();
                seg[i] = new Points(u, v, i + 1);
            }
            Arrays.sort(seg);
//        w.printLine(rem);
            TreeMap<Integer, ArrayList<Integer>> tm = new TreeMap<>();
            ArrayList<Integer> res = new ArrayList<>();
            int cur = 0, ptr = 0;
            for (int i = 0; i < 2e5 + 10; i++) {
                while (ptr < seg.length && seg[ptr].l == i) {
                    if (tm.containsKey(seg[ptr].r)) {
                        ArrayList<Integer> ad = tm.get(seg[ptr].r);
                        ad.add(seg[ptr].ind);
                        tm.put(seg[ptr].r, ad);
                    } else {
                        ArrayList<Integer> ad = new ArrayList<>();
                        ad.add(seg[ptr].ind);
                        tm.put(seg[ptr].r, ad);
                    }
                    ptr++;
                    cur++;
                }
                while (cur > k) {
                    Map.Entry<Integer, ArrayList<Integer>> ent = tm.pollLastEntry();
                    ArrayList<Integer> ad = ent.getValue();
                    if (ad.size() <= cur - k) {
                        res.addAll(ad);
                        cur -= ad.size();
                    } else {
                        ArrayList<Integer> tf = new ArrayList<>();
                        for (int j = 0; j < cur - k; j++) {
                            res.add(ad.get(j));
                        }
                        for (int j = cur - k; j < ad.size(); j++) {
                            tf.add(ad.get(j));
                        }
                        cur = k;
                        tm.put(ent.getKey(), tf);
                    }
                }
                if (tm.containsKey(i)) {
                    cur -= tm.get(i).size();
                    tm.remove(i);
                }
            }
            w.printLine(res.size());
            for (int indices : res) {
                w.print(indices + " ");
            }
            w.printLine();
        }

    }

    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 printLine() {
            writer.println();
        }

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

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

    }

    static class Points implements Comparable<Points> {
        int l;
        int r;
        int ind;

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

        public int compareTo(Points o) {
            if (this.l == o.l) {
                return this.r - o.r;
            }
            return this.l - o.l;
        }

    }
}