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.*;
import java.lang.*;
import java.io.*;

public class Main
{
	PrintWriter out = new PrintWriter(System.out);
	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tok = new StringTokenizer("");
    String next() throws IOException {
        if (!tok.hasMoreTokens()) { tok = new StringTokenizer(in.readLine()); }
        return tok.nextToken();
    }
    int ni() throws IOException { return Integer.parseInt(next()); }
    long nl() throws IOException { return Long.parseLong(next()); }
    
    static int[]ST;
    
    void solve() throws IOException {
        int n=ni(),k=ni();
        int[][]A=new int[n+1][2];
        int[]B=new int[n+1];
        int[][]C=new int[n+1][2];
        for (int x=0;x<n;x++) {
            A[x][0]=ni();
            A[x][1]=x+1;
            B[x+1]=ni();
            C[x][0]=B[x+1];
            C[x][1]=x+1;
        }
        A[n][0]=Integer.MAX_VALUE;
        C[n][0]=Integer.MAX_VALUE;
        
        Arrays.sort(A,(a,b)->Integer.compare(a[0],b[0]));
        Arrays.sort(C,(a,b)->Integer.compare(a[0],b[0]));
        
        ArrayList<Integer>F=new ArrayList();
        boolean[]G=new boolean[n+1];
        
        int sts = 1;
        while (sts<n) sts=sts<<1;
        ST=new int[sts*2];
        
        int p=0;
        int q=0;
        int r=0;
        int t=0;
        while (p<n) {
            q=A[p][0];
            while (C[r][0]<q) { 
                if (!G[C[r][1]]) t--; 
                r++; 
            }
            while (A[p][0]==q) {
                int nv=A[p][1];
                stadd(1,n,nv,B[nv],0);
                p++;
                t++;
            }
            while (t>k) {
                int nv=strem(1,n,0);
                G[nv]=true;
                F.add(nv);
                t--;
            }
        }
        
        out.println(F.size());
        for (int x=0;x<F.size();x++) out.print(F.get(x)+" ");
        out.println();
        out.flush();
    }
    
    void stadd(int l, int r, int v, int x, int ind) {
        if (l==r) {
            ST[ind] = x;
            return;
        }
        int m=mid(l,r);
        if (v<=m) stadd(l,m,v,x,2*ind+1);
        else stadd(m+1,r,v,x,2*ind+2);
        ST[ind]=Math.max(ST[2*ind+1],ST[2*ind+2]);
        return;
    }
    
    int mid(int l, int r) { return((l+r)/2); }
    
    int strem(int l, int r, int ind) {
        if (l==r) {
            ST[ind]=0;
            return r;
        }
        int rv=0;
        int m=mid(l,r);
        if (ST[2*ind+1]>ST[2*ind+2]) rv=strem(l,m,2*ind+1);
        else rv=strem(m+1,r,2*ind+2);
        ST[ind]=Math.max(ST[ind*2+1],ST[ind*2+2]);
        return rv;
    }
    
    public static void main(String[] args) throws IOException {
        new Main().solve();
    }
}