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;

public class Solution
{
    public static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        var N = (int)vals[0];
        var K = vals[1];
        var A = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var max = (int)Math.Log(K, 2) + 1;
        var AA = A.Concat(A).ToArray();
        // nexts[j][i] : iから2^j回分移動した位置

        var next = new long[N];
        var indexs = new Dictionary<int, int>(); // a -> index
        for (int i = 0; i < N * 2; i++)
        {
            var a = AA[i];
            if (indexs.ContainsKey(a))
            {
                var prev = indexs[a];
                if (prev < N)
                {
                    next[prev] = i + 1 - prev;
                }
            }
            indexs[a] = i;
        }

        var nexts = new long[max][];
        nexts[0] = next;
        for (int j = 1; j < max; j++)
        {
            nexts[j] = new long[N];
            for (int i = 0; i < N; i++)
            {
                var t = nexts[j - 1][i % N];
                nexts[j][i] = t + nexts[j - 1][(i + t) % N];
            }
        }

        long p = 0;
        for (var k = N * K - 1; k > N;)
        {
            for (int j = max - 1; j >= 0; j--)
            {
                if (nexts[j][p % N] < k)
                {
                    k -= nexts[j][p % N];
                    p += nexts[j][p % N];
                    break;
                }
            }
        }

        var list = new List<int>();
        indexs.Clear();
        for (p = (p == N * K) ? p : p % N; p < N; p++)
        {
            var a = A[p];
            if (!indexs.ContainsKey(a))
            {
                indexs[a] = list.Count;
                list.Add(a);
            }
            else
            {
                var index = indexs[a];
                foreach (var aa in list.Skip(index))
                {
                    indexs.Remove(aa);
                }
                list.RemoveRange(index, list.Count - index);
            }
        }

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