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.Scanner;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.util.Arrays;
import java.util.TreeSet;
import java.util.TreeMap;

public class Main {

     static StringBuffer strbf = new StringBuffer();

	public static void main(String[] args) throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		String[] input = reader.readLine().split(" ");
		int n = Integer.parseInt(input[0]), k = Integer.parseInt(input[1]);
		int[][] arr = new int[n][3];
		for(int i = 0; i < n; i++) {
		     input = reader.readLine().split(" ");
		     arr[i][0] = Integer.parseInt(input[0]);
		     arr[i][1] = Integer.parseInt(input[1]);
		     arr[i][2] = i + 1;
		}
		TreeMap<Integer, TreeSet<Integer>> map = new TreeMap<Integer, TreeSet<Integer>>();
		Arrays.sort(arr, (A, B) -> A[0] - B[0]);
		int size = 0;
		int ans = 0;
		for(int i = 0; i < n;) {
		     int curr = arr[i][0], j = i;
		     while(j < n && arr[j][0] == arr[i][0]) {
		          if(!map.containsKey(arr[j][1])) {
		               map.put(arr[j][1], new TreeSet<Integer>());
		          }
		          map.get(arr[j][1]).add(arr[j][2]);
		          size++;
		          j++;
		     }
		     while(map.size() > 0 && map.firstKey() < curr) {
		          int temp = map.firstKey();
		          size -= map.get(temp).size();
		          map.remove(temp);
		     }
		     while(size > k) {
		          int temp = map.lastKey();
		          if(map.get(temp).size() == 0) {
		               map.remove(temp);
		               continue;
		          }
		          size--;
		          ans++;
		          strbf.append(map.get(temp).first() + " ");
		          map.get(temp).remove(map.get(temp).first());
		     }
		     i = j;
		}
		System.out.println(ans);
		System.out.print(strbf.toString());

}
}