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: Accepted)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		string[] input = Console.ReadLine().Split(' ');
		int n = int.Parse(input[0]);
		long k = long.Parse(input[1]);
		int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
    int[] turns = new int[n];//それぞれの数のターン
    int a = 200001;
    List<int>[] positionList = new List<int>[a];
    for(int i = 0; i < a; i++) positionList[i] = new List<int>();
    int[] numsCount = new int[a];
    int[] numsNumber = new int[n];//それぞれの数は、何番目-1に出たものか

    for(int i = 0; i < n; i++)
    {
      positionList[nums[i]-1].Add(i);
      numsNumber[i] = numsCount[nums[i]-1];
      numsCount[nums[i]-1]++;
    }

    int lookingPosition = 0;
    int nowTurn = 1;
    while(true)
    {
      if(positionList[nums[lookingPosition]-1][positionList[nums[lookingPosition]-1].Count()-1]
        == lookingPosition)
      {
        nowTurn++;
        turns[lookingPosition] = nowTurn;
        lookingPosition = positionList[nums[lookingPosition]-1][0]+1;
        if(lookingPosition == n) break;
      }else
      {
        turns[lookingPosition] = nowTurn;
        lookingPosition 
          = positionList[nums[lookingPosition]-1][numsNumber[lookingPosition]+1]+1;
        if(lookingPosition == n) break;
      }
    }

    k %= nowTurn;
    if(k == 0) k += nowTurn;

    int leftPosition = 0;
    for(int i = 0; i < n; i++)
    {
      if(turns[i] == k)
      {
        if(numsNumber[i] != numsCount[nums[i]-1]-1)
        {
          leftPosition = Math.Max(leftPosition,positionList[nums[i]-1][numsNumber[i]+1]+1);
        }else leftPosition = Math.Max(leftPosition,positionList[nums[i]-1][0]+1);
      }
    }

    var stack = new Stack<int>();
    bool[] used = new bool[a];
    for(int i = leftPosition; i < n; i++)
    {
      if(!used[nums[i]])
      {
        stack.Push(nums[i]);
        used[nums[i]] = true;
      }else
      {
        while(true)
        {
          int topMemo = stack.Peek();
          used[topMemo] = false;
          stack.Pop();
          if(topMemo == nums[i]) break;
        }
      }
    }

    int aa = stack.Count;
    int[] answers = new int[aa];
    for(int i = 0; i < aa; i++)
    {
      int popMemo = stack.Peek();
      answers[aa-1-i] = popMemo;
      stack.Pop();
    }

    //Console.WriteLine(nowTurn+" "+turns[0]+" "+turns[1]+" "+turns[2]+" "+leftPosition);
		Console.WriteLine(string.Join(" ", answers));
	}
}