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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
public class Main {
    public static void main(String[] args){

        Scanner sc = new Scanner(System.in);
        // 整数の入力
        int N=sc.nextInt();
        long K=sc.nextLong();
        ArrayList<Integer> A=new ArrayList<>();
        ArrayList<ArrayList<Integer>>R=new ArrayList<>();
        for(int i=0;i<N;i++){
            A.add(sc.nextInt());
        }
        ArrayList<Integer>B=new ArrayList<>();
        do {
            B.addAll(A);
            for(int i=0;i<B.size();i++){
                Integer a=B.get(i);
                if(B.lastIndexOf(a)!=i){
                    B.set(i,null);
                    i++;
                    for(;i<=B.size();i++){
                        if(B.get(i).equals(a)){
                            B.set(i,null);
                            break;
                        }
                        B.set(i,null);
                    }
                }
            }
            B.removeAll(Collections.singleton(null));
            R.add(new ArrayList<Integer>(B));
            if(R.size()>K)
            {
                break;
            }

        }while(B.size()!=0);
        long loop=R.size();
        ArrayList<Integer> result=R.get((int)((K-1)%loop));
        StringBuilder br=new StringBuilder();
        for(int i :result){
            br.append(i);
            br.append(' ');
        }
        System.out.println(br.toString());



    }
}