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: Runtime Error)

using System;
using System.Collections.Generic;

namespace ConsoleApp1
{
    class Program
    {

        static int Search(List<int> indexes, int startindex)
        {
            int last = indexes[indexes.Count - 1];
            if (startindex >= last)
            {
                return indexes[0];
            }
            else
            {
                return indexes[indexes.FindIndex(x => x == startindex) + 1];
            }
        }

        static void Main(string[] args)
        {
            var s = Console.ReadLine().Split(' ');
            int n = int.Parse(s[0]);
            long k = long.Parse(s[1]);
            int[] a = new int[n];
            var tempamap = new Dictionary<int, List<int>>();
            var amap = new Dictionary<int, int[]>();
            var ss = Console.ReadLine().Split(' ');
            for (int i = 0; i < n; i++)
            {
                a[i] = int.Parse(ss[i]);
                if (tempamap.ContainsKey(a[i]))
                {
                    tempamap[a[i]].Add(i);
                }
                else
                {
                    var temp = new List<int>();
                    temp.Add(i);
                    tempamap.Add(a[i], temp);
                }
            }
            // 先頭の推移をみる
            int topindex = 0;
            int linecount = 0;
            int count = 0;
            int[] topindexes = new int[n];
            int[] linecounts = new int[n];
            int nexttopindex = Search(tempamap[a[topindex]], topindex) + 1;
            if (nexttopindex == n)
            {
                nexttopindex = 0;
            }
            if (nexttopindex <= topindex + 1)
            {
                linecount++;
            }
            bool hasfinished = false;
            int finaltopindex = -1;
            if (linecount >= k)
            {
                hasfinished = true;
                finaltopindex = 0;
            }
            count++;
            topindexes[count] = nexttopindex;
            linecounts[count] = linecount;
            topindex = nexttopindex;
            while (topindex != 0 && linecount < k)
            {
                nexttopindex = Search(tempamap[a[topindex]], topindex) + 1;
                if (nexttopindex == n)
                {
                    nexttopindex = 0;
                }
                if (nexttopindex <= topindex + 1)
                {
                    linecount++;
                }
                if (nexttopindex != 0)
                {
                    count++;
                    topindexes[count] = nexttopindex;
                    linecounts[count] = linecount;
                }
                if (linecount == k)
                {
                    hasfinished = true;
                    break;
                }
                topindex = nexttopindex;
            }
            if (finaltopindex < 0)
            {
                finaltopindex = topindex;
            }
            if (!hasfinished)
            {
                int leftline = (int)(k % linecount);
                finaltopindex = topindexes[Array.FindLastIndex(linecounts, x => x == leftline - 1 || x == leftline - 1 + linecount)];
            }
            // finaltopindexを含めてそこからの数列を作る
            var lasta = new List<int>();
            for (int i = finaltopindex; i < n; i++)
            {
                if (lasta.Contains(a[i]))
                {
                    int remindex = lasta.FindIndex(x => x == a[i]);
                    lasta.RemoveRange(remindex, lasta.Count - remindex);
                }
                else
                {
                    lasta.Add(a[i]);
                }
            }
            Console.WriteLine(string.Join(" ", lasta));
            

#if DEBUG
            Console.ReadKey();
#endif
        }
    }
}