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:
/* Rajkin Hossain */

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class D{
   
    FastInput k = new FastInput(System.in);
    //FastInput k = new FastInput("/home/rajkin/Desktop/input.txt");
    FastOutput z = new FastOutput();
    
    SegmentTree segTree;
    
    int n;
    int K;
    
    ArrayList<Pair> [] rightPoints;
    PriorityQueue<Triple> pq;
    
    void startAlgo() {
    	
		for(int i = 1; i<=n; i++) {
			int left = k.nextInt();
			int right = k.nextInt();
			
			rightPoints[left].add(new Pair(right, i));
			
			segTree.update(left, right, 1);
		}
		
		ArrayList<Integer> ans = new ArrayList<Integer>();
		
		for(int i = 1; i<=(int)(2e5); i++) {
			
			for(Pair p : rightPoints[i]) {
				pq.add(new Triple(i, p.rightPoint, p.rightIndex));
			}
			
			while(!pq.isEmpty() && segTree.getRanges(i) > K) {
				Triple t = pq.poll();
				
				segTree.update(t.left, t.right, -1);
				
				ans.add(t.rangeIndex);
			}
		}
		
		Collections.sort(ans);
		
		z.println(ans.size());
		
		for(int idx : ans) {
			z.print(idx+" ");
		}
		
		z.println();
    }
    
	void startProgram() {
		
		while(k.hasNext()) {
			n = k.nextInt();
			K = k.nextInt();
			
			rightPoints = new ArrayList[(int)(2e5) + 1];
			
			for(int i = 1; i<=(int)(2e5); i++) {
				rightPoints[i] = new ArrayList();
			}
			
			pq = new PriorityQueue<Triple>();
			
			segTree = new SegmentTree((int)(2e5));
			
			startAlgo();
		}
    	
    	z.flush();
    	System.exit(0);
    }
    
	class Pair{
		int rightPoint, rightIndex;
		
		public Pair(int rightPoint, int rightIndex) {
			super();
			this.rightPoint = rightPoint;
			this.rightIndex = rightIndex;
		}
	}
    
	class Triple implements Comparable<Triple>{
		Integer left, right;
		int rangeIndex;
		
		public Triple(int left, int right, int rightIndex) {
			super();
			this.left = left;
			this.right = right;
			this.rangeIndex = rightIndex;
		}

		@Override
		public int compareTo(Triple arg0) {
			return arg0.right - this.right;
		}
	}
	
	public class SegmentTree {
	    int [] tree;
	    int treeLength;
	    
	    int [] datas;
	   
	    public SegmentTree(int max_size) {
	        tree = new int[max_size * 4];
	        treeLength = max_size;
	    }
	       
	    public int getRanges(int index) {
	        return getRanges(1, 1, treeLength, index, 0);
	    }
	       
	    public int getRanges(int nodeId, int i, int j, int index, int propagation) {
	        if (i>index || j<index) {  
	            return 0;
	        }
	       
	        if (i>=index && j<=index) {
	            return tree[nodeId] + propagation;
	        }
	       
	        int left = nodeId * 2;
	        int right = nodeId * 2 + 1;
	        int mid = (i + j) / 2;
	        
	        int leftSum = getRanges(left, i, mid, index, tree[nodeId] + propagation);
	        int rightSum =  getRanges(right, mid+1, j, index, tree[nodeId] + propagation);
	        
	        return leftSum + rightSum;
	    }
		
	    public void update(int left, int right, int value) {
	        update(1, 1, treeLength, left, right, value);
	    }
	   
	    public void update(int nodeId, int i, int j, int b, int e, int value) {
	        if (j<b || i>e) {
	            return;
	        }
	       
	        if (i >= b && j <= e) {
	            tree[nodeId] += value;
	           
	            return;
	        }
	       
	        int left = nodeId * 2;
	        int right = nodeId * 2 + 1;
	        int mid = (i + j) / 2;
	       
	        update(left, i, mid, b, e, value);
	        update(right, mid + 1, j, b, e, value);
	    }
	}
    
    public static void main(String [] args) throws IOException {
        new Thread(null, new Runnable(){
            public void run(){
            	try{ 
            		new D().startProgram();
            	}
            	catch(Exception e){
            		e.printStackTrace();
            	}
            }
        },"Main",1<<28).start();
    }
    

    /* MARK: FastInput and FastOutput */
 
    class FastInput {
        BufferedReader reader;
        StringTokenizer tokenizer;
 
        FastInput(InputStream stream){
            reader = new BufferedReader(new InputStreamReader(stream));
        }
       
        FastInput(String path){
            try {
                reader = new BufferedReader(new FileReader(path));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            tokenizer = null;
        }
 
        String next() {
            return nextToken();
        }
       
        String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
           
            return null;
        }
 
        boolean hasNext(){
            try {
                return reader.ready();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return false;
        }
 
        String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = null;
                try {
                    line = reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(nextToken());
        }
       
        long nextLong() {
            return Long.valueOf(nextToken());
        }
        
        double nextDouble() {
            return Double.valueOf(nextToken());
        }
    }
 
    class FastOutput extends PrintWriter {
		FastOutput() {
			super(new BufferedOutputStream(System.out)); 
		}
		
		public void debug(Object...obj) {
		    System.err.println(Arrays.deepToString(obj));
		}
    }
}