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

public class Solver
{
    public void Solve()
    {
        int n = ri, k = ri;
        List<int> a = new List<int>();
        int t = -1;
        for (int i = 0; i < n; i++)
        {
            a.Add(ri);
            if (t > -1 && a[a.Count - 1] != a[a.Count - 2])
            {
                a.RemoveRange(t, a.Count - t - 2);
            }
            else if (t == -1 && a.Count > 1 && a[a.Count - 1] == a[a.Count - 2])
            {
                t = a.Count - 2;
            }
        }
        n = a.Count;
        List<int> s = new List<int>();
        string[] ss = new string[n+1];
        int m = n;
        for (int j=0;j<m;j++) {
            for (int i = 0; i < n; i++)
            {
                t = s.IndexOf(a[i]);
                if (t > -1)
                {
                    s.RemoveRange(t, s.Count - t);
                }
                else
                {
                    s.Add(a[i]);
                }
            }
            ss[j+1] = string.Join(" ", s);
            if (!s.Any()) { m = j + 1; }
        }
        Write(ss[k%m]);
    }

    int ri { get { return sc.Integer(); } }
    long rl { get { return sc.Long(); } }
    double rd { get { return sc.Double(); } }
    string rs { get { return sc.Scan(); } }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
    
    private const long mod = 1000000007;
    long Reverse(long n) { return Pow(n, mod - 2); }
    int Abs(int n) { return (n > 0) ? n : -n; }
    int Gcd(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = Gcd(p, n[i]); } return p; }
    int Gcd(int a, int b) { return (a == 0) ? b : Gcd(b % a, a); }
    int Lcm(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = Lcm(p, n[i]); } return p; }
    int Lcm(int a, int b) { return a * b / Gcd(a, b); }
    int Max(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = (p > n[i]) ? p : n[i]; } return p; }
    int Min(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = (p < n[i]) ? p : n[i]; } return p; }
    long Mul(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p * n[i]) % mod; } return p; }
    long Pow(long n, long p) { long t = n, q = 1; while (p > 0) { if (p % 2 == 1) { q = (q * t) % mod; } t = (t * t) % mod; p /= 2; } return q; }
    long PowUpper(long n, long b) { long p = 1; while (p <= n) { p *= b; } return p; }
    long Abs(long n) { return (n > 0) ? n : -n; }
    long Gcd(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = Gcd(p, n[i]); } return p; }
    long Gcd(long a, long b) { return (a == 0) ? b : Gcd(b % a, a); }
    long Lcm(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = Lcm(p, n[i]); } return p; }
    long Lcm(long a, long b) { return a * b / Gcd(a, b); }
    long Max(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p > n[i]) ? p : n[i]; } return p; }
    long Min(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p < n[i]) ? p : n[i]; } return p; }
    void Write<T>(T t) { Console.WriteLine(t.ToString()); }
    void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); }
    void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); }
    void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); }
}

static class Program
{
    static public void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}

public class StreamScanner
{
    public StreamScanner(Stream stream) { str = stream; }
    private readonly Stream str;
    private readonly byte[] buf = new byte[1024];
    private int len, ptr;
    public bool isEof = false;
    public bool IsEndOfStream { get { return isEof; } }
    private byte read()
    {
        if (isEof) throw new EndOfStreamException();
        if (ptr >= len)
        {
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) <= 0)
            {
                isEof = true;
                return 0;
            }
        }
        return buf[ptr++];
    }
    public char Char()
    {
        byte b = 0;
        do b = read();
        while (b < 33 || 126 < b);
        return (char)b;
    }
    public string Scan()
    {
        var sb = new StringBuilder();
        for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
            sb.Append(b);
        return sb.ToString();
    }
    public long Long()
    {
        long ret = 0; byte b = 0; var ng = false;
        do b = read();
        while (b != '-' && (b < '0' || '9' < b));
        if (b == '-') { ng = true; b = read(); }
        for (; true; b = read())
        {
            if (b < '0' || '9' < b)
                return ng ? -ret : ret;
            else ret = ret * 10 + b - '0';
        }
    }
    public int Integer() { return (int)Long(); }
    public double Double() { return double.Parse(Scan()); }
}