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:
//package round595;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.List;

public class D2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), K = ni();
		int[][] rs = new int[n][];
		for(int i = 0;i < n;i++){
			rs[i] = new int[]{ni(), ni()+1, i+1};
		}
		Arrays.sort(rs, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				return a[1] - b[1];
			}
		});
		
		StarrySkyTree sst = new StarrySkyTree(200005);
		List<Integer> anss = new ArrayList<>();
		for(int[] e : rs){
			int max = -sst.min(e[0], e[1]);
			if(max < K){
				sst.add(e[0], e[1], -1);
			}else{
				anss.add(e[2]);
			}
		}
		out.println(anss.size());
		for(int v : anss){
			out.print(v + " ");
		}
		out.println();
	}
	
	public static class StarrySkyTree {
		public int M, H, N;
		public int[] st;
		public int[] plus;
		public int I = Integer.MAX_VALUE/2; // I+plus<int
		
		public StarrySkyTree(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(n-1, 1))<<2;
			H = M>>>1;
			st = new int[M];
			plus = new int[H];
		}
		
		public StarrySkyTree(int[] a)
		{
			N = a.length;
			M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
			H = M>>>1;
			st = new int[M];
			for(int i = 0;i < N;i++){
				st[H+i] = a[i];
			}
			plus = new int[H];
			Arrays.fill(st, H+N, M, I);
			for(int i = H-1;i >= 1;i--)propagate(i);
		}
		
		private void propagate(int i)
		{
			st[i] = Math.min(st[2*i], st[2*i+1]) + plus[i];
		}
		
		public void add(int l, int r, int v){ if(l < r)add(l, r, v, 0, H, 1); }
		
		private void add(int l, int r, int v, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				if(cur >= H){
					st[cur] += v;
				}else{
					plus[cur] += v;
					propagate(cur);
				}
			}else{
				int mid = cl+cr>>>1;
				if(cl < r && l < mid){
					add(l, r, v, cl, mid, 2*cur);
				}
				if(mid < r && l < cr){
					add(l, r, v, mid, cr, 2*cur+1);
				}
				propagate(cur);
			}
		}
		
		public int min(int l, int r){ return l >= r ? I : min(l, r, 0, H, 1);}
		
		private int min(int l, int r, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				return st[cur];
			}else{
				int mid = cl+cr>>>1;
				int ret = I;
				if(cl < r && l < mid){
					ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
				}
				if(mid < r && l < cr){
					ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
				}
				return ret + plus[cur];
			}
		}
		
		public void fall(int i)
		{
			if(i < H){
				if(2*i < H){
					plus[2*i] += plus[i];
					plus[2*i+1] += plus[i];
				}
				st[2*i] += plus[i];
				st[2*i+1] += plus[i];
				plus[i] = 0;
			}
		}
		
		public int firstle(int l, int v) {
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2|cur>>>j&1;
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur;
					}else{
						return cur-H;
					}
				}else{
					cur++;
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
				}
			}
		}
		
		public int lastle(int l, int v) {
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2|cur>>>j&1;
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur+1;
					}else{
						return cur-H;
					}
				}else{
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
					cur--;
				}
			}
		}
		
		public int[] toArray() { return toArray(1, 0, H, new int[H]); }
		
		private int[] toArray(int cur, int l, int r, int[] ret)
		{
			if(r-l == 1){
				ret[cur-H] = st[cur];
			}else{
				toArray(2*cur, l, l+r>>>1, ret);
				toArray(2*cur+1, l+r>>>1, r, ret);
				for(int i = l;i < r;i++)ret[i] += plus[cur];
			}
			return ret;
		}
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D2().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}