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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader sc = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, sc, out);
        out.close();
    }

    static class Task {
    	public Node[] buf;
    	
    	public int lower_bound(int[] L,int l,int r,int x) {
    		int ans=-1;
    		while(l<=r) {
    			int mid=(l+r)>>1;
    		    if(L[mid]>=x) {
    		    	r=mid-1;
    		    	ans=mid;
    		    }
    		    else
    		    	l=mid+1;
    		}
    		return ans;
    	}
    	
        public void solve(int testNumber, InputReader sc, PrintWriter out) throws IOException {
        	int n=sc.nextInt();
        	int k=sc.nextInt();
        	buf=new Node[n+1];
        	Point[] point=new Point[n+1];
        	ArrayList<Integer> res=new ArrayList<Integer>();
        	int[] L=new int[n+1];
        	BIT bit=new BIT((int) 2e5);
        	for(int i=1;i<=n;i++) {
        		int l=sc.nextInt();
        		int r=sc.nextInt();
        		buf[i]=new Node(l,r,i);
        		bit.add(l, r, 1);
        	}
        	Arrays.sort(buf,1,n+1);
        	for(int i=1;i<=n;i++) {
        		L[i]=buf[i].l;
        		point[i]=new Point(buf[i].r,buf[i].index,i);
        	}
        	SegTree sgt=new SegTree(n,point);
        	sgt.build(1, 1, n);
        	for(int i=1;i<=200000;i++) {
        		while(bit.ask(i)>k) {
        			/*int maxIndex=Arrays.binarySearch(L, 1, n+1, i+1);
        			if(maxIndex<0)
        				maxIndex=-(maxIndex+1);
        			maxIndex--;*/
        			int maxIndex=lower_bound(L,1,n,i+1)-1;
        			if(maxIndex<0)
        				maxIndex=n;
        			//System.out.println(maxIndex);
        			Point temp=sgt.ask(1, 1, maxIndex);
        			//System.out.println(i+" "+L[maxIndex]+" "+(maxIndex+1>n?L[maxIndex]:L[maxIndex+1]));
        		/*	System.out.println("f: "+L[temp.nowIndex]+" "+temp.r);
        			System.out.println("s: "+i+" "+temp.r);*/
        			bit.add(L[temp.nowIndex], temp.r, -1);
        			res.add(temp.index);
        			sgt.change(1, temp.nowIndex);
        		}
        	}
        	out.println(res.size());
        	for(int v:res)
        		out.print(v+" ");
        	out.println();
        }

    }
    
    static class Node implements Comparable<Node>{
    	int l;
    	int r;
    	int index;
    	
    	public Node(int l,int r,int index) {
    		this.l=l;
    		this.r=r;
    		this.index=index;
    	}

		@Override
		public int compareTo(Node o) {
			if(this.l!=o.l)
				return this.l-o.l;
			return this.r-o.r;
		}
    }
    
    static class BIT{
		public long[] C;
		
		public BIT(int n) {
			C=new long[n+1];
		}
		
		public int lowBit(int x) {
			return x&(-x);
		}
		
		public void add(int x,long y) {
			for(int i=x;i<C.length;i+=lowBit(i)) {
				C[i]+=y;
			}
		}
		
		public long ask(int x) {
			long res=0;
			
			for(int i=x;i>0;i-=lowBit(i))
				res+=C[i];
			
			return res;
		}
		
		//C[i]表示i这个数有C[i]个，相当于权值BIT，查询第k大。
	    public int kth_element(int k) {
	        int p = 0;
	        for (int lim = 1 << 20; lim>0; lim /= 2)
	            if (p + lim < C.length && C[p + lim] < k) {
	                p += lim;
	                k -= C[p];
	            }
	        return p + 1;
	    }
	    
	    public void add(int l,int r,long val) {
	    	this.add(l, val);
	    	this.add(r+1, -val);
	    }
	    
	    public long ask(int l,int r) {
	    	return this.ask(r)-this.ask(l-1);
	    }
	}
    
    static class SegTree{
    	class Node{
    		int l;
    		int r;
    	    Point val;
    	    
    	    public Node(int l,int r) {
    	    	this.l=l;
    	    	this.r=r;
    	    }
    	}
    	public Node[] t;
    	public Point[] A;
    	
    	public SegTree(int n,Point[] A) {
    		 this.t=new Node[(n+10)<<4];
    		 this.A=A;
    	}
    	
    	public void pushUp(int p) {
    		if(t[p*2+1].val==null&&t[p*2].val==null) {
    			t[p].val=null;
    			return ;
    		}
    		if(t[p*2].val==null) {
    			t[p].val=t[p*2+1].val.clone();
    			return ;
    		}
    		if(t[p*2+1].val==null) {
    			t[p].val=t[p*2].val.clone();
    			return ;
    		}
    		if(t[p*2].val.r>=t[p*2+1].val.r)
    			t[p].val=t[p*2].val.clone();
    		else
    			t[p].val=t[p*2+1].val.clone();
    	}
    	
    	public void build(int p,int l,int r) {
    		t[p]=new Node(l,r);
    		if(l==r) {
    			t[p].val=A[l];
    			return ;
    		}
    		int mid=(l+r)>>1;
    		 build(p*2,l,mid);
    		 build(p*2+1,mid+1,r);
    		 pushUp(p);
    	}
    	
    	public void change(int p,int index) {
    		if(t[p].l==t[p].r) {
    			t[p].val=null;
    			return ;
    		}
    		int mid=(t[p].l+t[p].r)>>1;
	        if(index<=mid)
	        	change(p*2,index);
	        else
	        	change(p*2+1,index);
	        pushUp(p);
    	}
    	
    	public Point ask(int p,int l,int r) {
    		if(t[p].l>=l&&t[p].r<=r) 
    			return t[p].val==null?null:t[p].val.clone();
    		Point res1=null;
    		Point res2=null;
    		int mid=(t[p].l+t[p].r)>>1;
    		if(l<=mid)
    			res1=ask(p*2,l,r);
    		if(r>mid)
    			res2=ask(p*2+1,l,r);
    		if(res1==null)
    			return res2;
    		if(res2==null)
    			return res1;
    		return res1.r>=res2.r?res1:res2;
    	}
    }
    
    static class Point{
    	int r;
    	int index;
    	int nowIndex;
    	
    	public Point(int r,int index,int nowIndex) {
    		this.r=r;
    		this.index=index;
    		this.nowIndex=nowIndex;
    	}
    	
    	@Override
    	public Point clone() {
			return new Point(r,index,nowIndex);
    	}
    }
    

    static class InputReader{
        StreamTokenizer tokenizer;
        public InputReader(InputStream stream){
            tokenizer=new StreamTokenizer(new BufferedReader(new InputStreamReader(stream)));
            tokenizer.ordinaryChars(33,126);
            tokenizer.wordChars(33,126);
        }
        public String next() throws IOException {
            tokenizer.nextToken();
            return tokenizer.sval;
        }
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        public boolean hasNext() throws IOException {
            int res=tokenizer.nextToken();
            tokenizer.pushBack();
            return res!=tokenizer.TT_EOF;
        }
        
        public double nextDouble() throws NumberFormatException, IOException {
        	return Double.parseDouble(next());
        }
        
        public BigInteger nextBigInteger() throws IOException {
        	return new BigInteger(next());
        }
    }
}