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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
namespace AGC036B
{
    class Program
    {
        static void Main(string[] args)
        {
            var matches = Regex.Matches(Console.ReadLine(), "[0-9]+");
            var N = long.Parse(matches[0].Value);
            var K = long.Parse(matches[1].Value);
            var A = Regex.Matches(Console.ReadLine(), "[0-9]+").Cast<Match>().Select(item=>int.Parse(item.Value)).ToList();
            var footprints = new List<List<int>>();

            var state = new List<int>();
             long repeatIndex = 0;
            long lastIndex = 0;
            bool find = false;

            for(long i = 0; i < K; i++)
            {
                foreach (var item in A)
                {
                    if (state.Contains(item)) state = state.TakeWhile(it => it != item).ToList();
                    else state.Add(item);
                }
                var c = 0;

                foreach (var f in footprints)
                {
                    if (Check(f, state)) { repeatIndex = c;lastIndex = i; find = true; goto AFTER; }
                    c++;
                }
                if (find) break;
                footprints.Add(state.Select(p=>p).ToList());
            }
            AFTER:
            if (find)
            {
                state = footprints[(int)((K - 1 - repeatIndex) % (lastIndex - repeatIndex) + repeatIndex)];
            }
            Console.WriteLine(string.Join(" ", state));
        }
        static bool Check(List<int> r, List<int> l)
        {
            var n = r.Count;
            if (l.Count != n) return false;
            for (var i = 0; i < n; i++)
            {
                if (r[i] != l[i]) return false;
            }
            return true;
        }

    }
}