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;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            var nk = Array.ConvertAll(Console.ReadLine().Split(), Convert.ToInt64);
            long n = nk[0], k = nk[1];
            var a = Array.ConvertAll(Console.ReadLine().Split(), Convert.ToInt32).ToList();
            List<int> ls = new List<int>();
            int time = 0;
            while (true)
            {
                for (int i = 0; i < a.Count; i++)
                    if (ls.Contains(a[i]))
                    {
                        int t = ls.FindIndex(x => x == a[i]);
                        ls.RemoveRange(t, ls.Count - t);
                    }
                    else ls.Add(a[i]);
                time++;
                if (ls.Count == 0) break;
            }
            long l = k % time;
            while (l-->0)
            {
                for (int i = 0; i < a.Count; i++)
                    if (ls.Contains(a[i]))
                    {
                        int t = ls.FindIndex(x => x == a[i]);
                        ls.RemoveRange(t, ls.Count - t);
                    }
                    else ls.Add(a[i]);
            }
            Console.WriteLine(string.Join(" ", ls));
        }
    }
}