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.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;

public class TooManySegments {

	static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
	static BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));

	static int n, k;
	static pair[] seg;

	static int N = 200002;

	static pair pair(int x, int y) {
		return new pair(x, y);
	}

	static class pair {
		int x;
		int y;
		
		public pair(int x, int y) {
			super();
			this.x = x;
			this.y = y;
		}

		public boolean equals(Object obj) {
    		if(obj == null || obj.getClass()!= this.getClass()) return false;
            pair p = (pair) obj;
            return (this.x==p.x && this.y==p.y);
        }
	}

	@SuppressWarnings("unchecked")
	static void process() throws Exception {
		List[] pos = new List[N];
		
		for (int i = 0; i < n; i++) {
			if (pos[seg[i].x] == null) {
				pos[seg[i].x] = new LinkedList<pair>();
			}
			pos[seg[i].x].add(pair(seg[i].y, i));
		}
		
		TreeSet<pair> set = new TreeSet<>((p1, p2) -> {
			if (p1.x == p2.x) {
				return p1.y - p2.y;
			}
			return p1.x - p2.x;
		});
		
		List<Integer> ans = new ArrayList<>();
		
		for (int i = 0; i < N; i++) {
			if (pos[i] != null) {
				for (pair p: (List<pair>) pos[i]) {
					set.add(p);
				}
			}
			while (!set.isEmpty() && set.first().x < i) {
				set.pollFirst();
			}
			
			while (set.size() > k) {
				pair p = set.pollLast();
				ans.add(p.y + 1);
			}
		}
		
		writer.write(String.format("%d", ans.size()));
		writer.newLine();
		for (int i: ans) {
			writer.write(String.format("%d ", i));
		}
		writer.newLine();
	}

	public static void main(String[] args) throws Exception {
		//		writer = new BufferedWriter(new FileWriter("output.txt"));
		String data[], input;
		data = reader.readLine().split(" ");
		n = Integer.parseInt(data[0]); k = Integer.parseInt(data[1]);
		seg = new pair[n];
		for (int i = 0; i < n; i++) {
			data = reader.readLine().split(" ");
			seg[i] = pair(Integer.parseInt(data[0]) - 1, Integer.parseInt(data[1]) - 1);
		}
		process();
		writer.close();
	}

}