Problem:
Score : 700 points

Problem Statement

We have a sequence of N \times K integers: X=(X_0,X_1,\cdots,X_{N \times K-1}).
Its elements are represented by another sequence of N integers: A=(A_0,A_1,\cdots,A_{N-1}). For each pair i, j (0 \leq i \leq K-1,\ 0 \leq j \leq N-1), X_{i \times N + j}=A_j holds.

Snuke has an integer sequence s, which is initially empty.
For each i=0,1,2,\cdots,N \times K-1, in this order, he will perform the following operation:

If s does not contain X_i: add X_i to the end of s.

If s does contain X_i: repeatedly delete the element at the end of s until s no longer contains X_i. Note that, in this case, we do not add X_i to the end of s.

Find the elements of s after Snuke finished the operations.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq K \leq 10^{12}

1 \leq A_i \leq 2 \times 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_0 A_1 \cdots A_{N-1}

Output

Print the elements of s after Snuke finished the operations, in order from beginning to end, with spaces in between.

Sample Input 1

3 2
1 2 3

Sample Output 1

2 3

In this case, X=(1,2,3,1,2,3).
We will perform the operations as follows:

i=0: s does not contain 1, so we add 1 to the end of s, resulting in s=(1).

i=1: s does not contain 2, so we add 2 to the end of s, resulting in s=(1,2).

i=2: s does not contain 3, so we add 3 to the end of s, resulting in s=(1,2,3).

i=3: s does contain 1, so we repeatedly delete the element at the end of s as long as s contains 1, which causes the following changes to s: (1,2,3)→(1,2)→(1)→().

i=4: s does not contain 2, so we add 2 to the end of s, resulting in s=(2).

i=5: s does not contain 3, so we add 3 to the end of s, resulting in s=(2,3).

Sample Input 2

5 10
1 2 3 2 3

Sample Output 2

3

Sample Input 3

6 1000000000000
1 1 2 2 3 3

Sample Output 3

s may be empty in the end.

Sample Input 4

11 97
3 1 4 1 5 9 2 6 5 3 5

Sample Output 4

9 2 6

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
		static void Main(){
		Sc sc=new Sc();
		var s=sc.La;
		int n=(int)s[0];
		int[] a=sc.Ia;
		int[] k=new int[200001];
		k=new int[200001];
		int[] g=Enumerable.Repeat(-1,n).ToArray();
		int[] h=Enumerable.Repeat(-1,200001).ToArray();
		for(int i = n-1;i>=0;i--) {
			if(h[a[i]]!=-1){g[i]=h[a[i]];}
			h[a[i]]=i;
		}
		for(int i = n-1;i>=0;i--) {
			if(g[i]==-1){g[i]=h[a[i]];}
		}
		int p=0,b=0;
		while(p<s[1]){
			if(g[b]<=b){p++;}
			b=(g[b]+1)%n;
			if(b==0){p++;}
			k[p]=b;
			if(b==0){break;}
		}
		s[1]--;
		if(p!=s[1]){s[1]%=p;}

		var avl=new Avl();
		var bb=new bool[200001];
		for(int i = k[s[1]];i<n;i++) {
			if(!bb[a[i]]){
				avl.Ud(i,a[i]);
				bb[a[i]]=true;
			}
			else{
				var q=avl.Ra(avl.cnt);
				while(q!=null){
					bb[q.d]=false;
					avl.Dl(q.n);
					if(q.d==a[i]){break;}
					q=avl.Ra(avl.cnt);
				}
			}
		}
		StringBuilder sb=new StringBuilder();
		while(avl.cnt>0){
			var q=avl.Ra(1);
			sb.Append(avl.Ra(1).d);
			if(avl.cnt!=1){sb.Append(" ");}
			else{sb.Append("\n");}
			avl.Dl(q.n);
		}
		Console.Write(sb);
	}
}
public class Avl{
	public class Nd{
		public int h=1,c=1;
		public readonly int n;
		public int d,ds;
		public Nd l,r;
		public Nd(int n,int d,Nd l,Nd r){this.n=n;this.d=d;ds=d;this.l=l;this.r=r;}
	}
	public Nd root,du;
	public int cnt=0;
	public Avl(){
		du=new Nd(int.MinValue,0,du,du);du.h=0;du.c=0;
		root=du;
	}
	public void Ud(int n,int d){
		Nd mn=new Nd(n,d,du,du);
		if(root==du){root=mn;}
		else{
			Fu(root,n,mn);
			if(Abs(root.l.h-root.r.h)>1){root=Rotate(root);}
		}
		cnt++;
	}
	private void Fu(Nd t,int n,Nd mn){
		t.c++;
		t.ds+=mn.d;
		if(t.n>n){
			if(t.l!=du){
				Fu(t.l,n,mn);
				if(Abs(t.l.l.h-t.l.r.h)>1){t.l=Rotate(t.l);}
			}
			else{t.l=mn;}
		}
		else{
			if(t.r!=du){
				Fu(t.r,n,mn);
				if(Abs(t.r.l.h-t.r.r.h)>1){t.r=Rotate(t.r);}
			}
			else{t.r=mn;}
		}
		t.h=Max(t.l.h,t.r.h)+1;
	}
	private Nd Rotate(Nd t){
		Nd nd=du;
		if(t.l.h>t.r.h){
			if(t.l.l.h>t.l.r.h){
				nd=t.l;t.l=t.l.r;nd.r=t;
				Ft(t);
			}
			else{
				nd=t.l.r;
				t.l.r=nd.l;nd.l=t.l;
				Ft(t.l);
				t.l=nd.r;nd.r=t;
				Ft(t);
			}
		}
		else{
			if(t.r.l.h>t.r.r.h){
				nd=t.r.l;
				t.r.l=nd.r;nd.r=t.r;
				Ft(t.r);
				t.r=nd.l;nd.l=t;
				Ft(t);
			}
			else{
				nd=t.r;t.r=t.r.l;nd.l=t;
				Ft(t);
			}
		}
		Ft(nd);
		return nd;
	}
	private void Ft(Nd t){
		t.h=Max(t.l.h,t.r.h)+1;
		t.c=t.l.c+t.r.c+1;
		t.ds=t.l.ds+t.r.ds+t.d;
	}
	public bool Dl(int n){
		Nd t=root;
		if(t.n==n){
			root=Fd2(root);
			if(cnt==0){return true;}
			else if(Abs(root.l.h-root.r.h)>1){root=Rotate(root);}
			else{Ft(root);}
			return true;
		}
		bool bo=Fd1(root,n);
		if(Abs(root.l.h-root.r.h)>1){root=Rotate(root);}
		else{Ft(root);}
		return bo;
	}
	private bool Fd1(Nd t,int n){
		if(t.n>n){
			if(t.l==du){return false;}
			else if(t.l.n!=n){
				bool bo=Fd1(t.l,n);
				if(Abs(t.l.l.h-t.l.r.h)>1){t.l=Rotate(t.l);}
				else{Ft(t.l);}
				return bo;
			}
			else{
				t.l=Fd2(t.l);
				Ft(t);
				return true;
			}
		}
		else{
			if(t.r==du){return false;}
			else if(t.r.n!=n){
				bool bo=Fd1(t.r,n);
				if(Abs(t.r.l.h-t.r.r.h)>1){t.r=Rotate(t.r);}
				else{Ft(t.r);}
				return bo;
			}
			else{
				t.r=Fd2(t.r);
				Ft(t);
				return true;
			}
		}
	}
	private Nd Fd2(Nd dn){
		cnt--;
		if(dn.l==du){return dn.r;}
		if(dn.r==du){return dn.l;}
		Nd u=dn.l;
		if(u.r==du){
			u.r=dn.r;
			Ft(u);
			return u;
		}
		u=Fd3(u,dn);
		if(Abs(dn.l.l.h-dn.l.r.h)>1){u.l=Rotate(dn.l);}
		else{Ft(dn.l);}
		Ft(u);
		return u;
	}
	private Nd Fd3(Nd u,Nd dn){
		if(u.r.r!=du){
			Nd v=Fd3(u.r,dn);
			if(Abs(u.r.l.h-u.r.r.h)>1){u.r=Rotate(u.r);}
			else{Ft(u.r);}
			return v;
		}
		else{
			Nd v=u.r;u.r=u.r.l;v.l=dn.l;v.r=dn.r;
			return v;
		}
	}
	public Nd Ra(int n){return cnt>=n?Fr(root,n):null;}
	private Nd Fr(Nd t,int n){
		if(t.l.c>n-1){return Fr(t.l,n);}
		if(t.l.c<n-1){return Fr(t.r,n-t.l.c-1);}
		return t;
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}