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.Collections.Generic;
using System.ComponentModel;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Text;

class Program
{
    private int N;
    private long K;
    private int[] A;

    static void Main(string[] args)
    {
        new Program().Solve();
    }

    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        K = sc.NextLong();
        A = sc.IntArray();

        var nextIndex = new int[N];
        var map = new Dictionary<int, int>();
        var b = new bool[N];
        for (int i = 0; i < N; i++)
        {
            int o;
            if (map.TryGetValue(A[i], out o))
            {
                nextIndex[o] = i;
                b[o] = true;
            }

            map[A[i]] = i;
        }

        for (int i = 0; i < N; i++)
        {
            int o;
            if (map.TryGetValue(A[i], out o))
            {
                if (!b[o])
                {
                    nextIndex[o] = i + N;
                    b[o] = true;
                }
            }
        }


        int index = 0;
        long cnt = 1;
        bool flag = false;
        while (true)
        {
            int next = nextIndex[index];
            //Console.WriteLine($"{index} {next}");

            if (next >= N)
            {
                cnt++;
                //Console.WriteLine($"I {next}");
            }
            if (next % N == N - 1)
            {
                break;
            }



            index = (next + 1) % N;
        }

        K %= cnt;
        // Console.WriteLine(cnt);
        index = 0;
        cnt = 0;

        if (K == 0)
        {
            Console.WriteLine();
            return;
        }
        while (true)
        {
            int next = nextIndex[index];
            if (next >= N)
            {
                cnt++;
            }

            if (cnt >= K)
            {
                break;
            }

            index = (next + 1) % N;
        }
        // Console.WriteLine(index);
        var stack = new Stack<int>();
        var hs = new HashSet<int>();
        for (int i = index; i < N; i++)
        {
            if (hs.Add(A[i]))
            {
                stack.Push(A[i]);
            }
            else
            {
                while (true)
                {
                    int p = stack.Pop();
                    hs.Remove(p);
                    if (p == A[i])
                    {
                        break;
                    }
                }
            }
        }

        Console.WriteLine(string.Join(" ", hs));
    }
}

class Scanner
{
    public Scanner()
    {
        _stream = new StreamReader(Console.OpenStandardInput());
        _pos = 0;
        _line = new string[0];
    }

    const char Separator = ' ';
    private readonly StreamReader _stream;
    private int _pos;
    private string[] _line;

    #region スペース区切りで取得

    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = _stream.ReadLine().Split(Separator);
            _pos = 0;
        }

        return _line[_pos++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }

    #endregion

    #region 型変換

    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }

    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }

    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }

    #endregion

    #region 配列取得

    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = _stream.ReadLine().Split(Separator);

        _pos = _line.Length;
        return _line;
    }

    public int[] IntArray()
    {
        return ToIntArray(Array());
    }

    public long[] LongArray()
    {
        return ToLongArray(Array());
    }

    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }

    #endregion
}