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.Linq;
using System.Text;

static class Program
{
    static int Cycle(int N, int[] next)
    {
        int i = 0;
        int cnt = 1;
        while (i < N)
        {
            if (next[i] <= i) { ++cnt; }
            i = next[i] + 1;
        }
        return cnt;
    }

    static int[] Make(int N, int[] A, int[] next, int cnt)
    {
        if (cnt == 0) { return new int[] { }; }
        int i = 0;
        while (cnt > 1)
        {
            if (next[i] <= i || next[i] + 1 == N) { --cnt; }
            i = (next[i] + 1) % N;
        }
        var list = new List<int>();
        while (i < N)
        {
            if (next[i] > i)
            {
                i = next[i] + 1;
            }
            else
            {
                list.Add(A[i]);
                ++i;
            }
        }
        return list.ToArray();
    }

    static int[] Solve(int N, long K, int[] A)
    {
        var next = new int[N];
        var dict = new Dictionary<int, List<int>>();
        for (int i = 0; i < N; ++i)
        {
            if (!dict.ContainsKey(A[i])) { dict[A[i]] = new List<int>(); }
            dict[A[i]].Add(i);
        }
        foreach (var list in dict.Values)
        {
            int C = list.Count;
            for (int i = 0; i < C; ++i)
            {
                next[list[i]] = list[(i + 1) % C];
            }
        }
        int cycle = Cycle(N, next);
        return Make(N, A, next, (int)(K % cycle));
    }

    static void Main(string[] args)
    {
        var V1 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
        var A = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        Console.WriteLine(string.Join(" ", Solve((int)V1[0], V1[1], A)));
    }
}