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.util.*;
import java.io.*;
import java.math.BigInteger;
 
public class Main
{
	static final int mod = (int)1e9+7;
	static int N = (int)2e6 + 2;
	public static void main(String[] args) throws Exception
	{
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		int k = in.nextInt();
		int[] line = new int[N];
		pair[] segments = new pair[n];
		for(int i = 0; i < n; i++)
		{
			segments[i] = new pair(in.nextInt(), in.nextInt(), i);
		}
		Arrays.sort(segments);
		TreeMap<Integer, Queue<Integer>> tm = new TreeMap();
		int j = 0;
		ArrayList<Integer> ans = new ArrayList();
		for(int i = 1; i < N; i++)
		{
			while(j < n && segments[j].f == i)
			{
				line[segments[j].f]++;
				line[segments[j].s + 1]--;
				Queue<Integer> q = tm.getOrDefault(segments[j].s, new LinkedList());
				q.add(segments[j].ind + 1);
				tm.put(segments[j].s, q);
				j++;
			}
			line[i] += line[i - 1];
			// System.out.println(total);
			if(line[i] <= k)
				continue;
			while(line[i] > k)
			{
				Map.Entry<Integer, Queue<Integer>> e = tm.lastEntry();
				Queue<Integer> q = e.getValue();
				ans.add(q.poll());
				if(q.size() == 0)
					tm.remove(e.getKey());
				line[i]--;
				line[e.getKey() + 1]++;
			}
		}
		out.println(ans.size());
		for(int i = 0; i < ans.size(); i++)
			out.print(ans.get(i) + " ");
		out.flush();
	}

	static class pair implements Comparable<pair>
	{
		int f, s, ind;

		public pair(int a, int b, int c)
		{
			f = a;
			s = b;
			ind = c;
		}

		public int compareTo(pair p)
		{
			return Integer.compare(f, p.f);
		}
	}
}
 
class FastReader
{
	BufferedReader br;
	StringTokenizer st;
 
	public FastReader()
	{
	    br = new BufferedReader(new InputStreamReader(System.in));
	}
 
	public String next() throws IOException
	{
	    if(st == null || !st.hasMoreElements())
	    {
	        st = new StringTokenizer(br.readLine());
	    }

	    return st.nextToken();
	}
 
	public int nextInt() throws IOException
	{
	    return Integer.parseInt(next());
	}
 
	public long nextLong() throws IOException
	{
	    return Long.parseLong(next());
	}
 
	public String nextLine() throws IOException
	{
		return br.readLine();
	}
}