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 javax.swing.text.Segment;
import java.util.*;
import java.io.*;
public class D595
{
    public static void main(String [] args)
    {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int MAXN = 2 * 100000 + 10;
        int n = sc.nextInt(); int k = sc.nextInt(); int [] s = new int [MAXN]; Segment [] seg = new Segment[n];
        for (int i = 0; i < n; i++) {
            int a = sc.nextInt(); int b = sc.nextInt();
            s[a]++; s[b+1]--;
            seg[i] = new Segment(a, b, i + 1);
        }
        Arrays.sort(seg, Comparator.comparingInt(o -> o.start)); int toAdd = 0;
        TreeSet<Segment> set = new TreeSet<>(); FenwickTree removed = new FenwickTree(MAXN);
        Set<Integer> ans = new HashSet<>();
        for (int i = 1; i < s.length; i++) {
            s[i] += s[i-1];
        }
        for (int i = 1; i < MAXN; i++) {
            if (removed.rangeSum(i, MAXN - 1) > 0) {
                s[i] -= removed.rangeSum(i, MAXN - 1);
            }
            while (toAdd < seg.length && seg[toAdd].start == i) {
                set.add(seg[toAdd]);
                toAdd++;
            }
            while (s[i] > k) {
                Segment largestEnd = set.pollFirst();
                ans.add(largestEnd.index);
                removed.update(largestEnd.end, 1);
                s[i]--;
            }
        }
        out.println(ans.size());
        for (Integer x: ans) {
            out.print(x + " ");
        }
        out.close();
    }
    static class Segment implements Comparable<Segment> {
        int start; int end; int index;
        Segment(int start, int end, int index) {
            this.start = start; this.end = end; this.index = index;
        }

        @Override
        public int compareTo(Segment o) {
            if (o.end == end) {
                if (o.start == start) {
                    return index - o.index;
                } else {
                    return o.start - start;
                }
            }
            return o.end - end;
        }
    }

    static class FenwickTree
    {
        int size;
        int [] table;

        FenwickTree(int size)
        {
            table = new int [size];
            this.size = size;
        }

        void init(int [] nums)
        {
            for (int i = 1; i < nums.length; i++)
            {
                update(i, nums[i]);
            }
        }

        void update(int i, int delta)
        {
            while (i < size)
            {
                table[i] += delta;
                i += Integer.lowestOneBit(i);
            }
        }

        int sum(int i)
        {
            int sum = 0;
            while (i > 0)
            {
                sum += table[i];
                i -= Integer.lowestOneBit(i);
            }
            return sum;
        }

        int rangeSum(int i, int j)
        {
            return sum(j) - sum(i - 1);
        }
    }






    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }



    }

}