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: Runtime Error)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		long K = sc.nextLong();

		ArrayList<Integer> X = new ArrayList<>();
		ArrayList<Integer> s = new ArrayList<>();

		for (int n = 0; n < N; n++) {
			X.add(sc.nextInt());
			if (X.size() > 1 && X.get(X.size() - 1) == X.get(X.size() - 2)) { // 同じ数字が隣接していれば消す
				X.remove(X.size() - 1);
				X.remove(X.size() - 1);
			}
		}
		
		// Xが空になら終了
		if(X.isEmpty()) {
			System.exit(0);
		}

		for (int i = 0; i < N * K; i++) {
			if (s.isEmpty()) { // sが空なら追加
				s.add(X.get(i % N));
			} else if (s.get(0) == X.get(i % N)) { // sの先頭が一致したら全要素削除
				s.clear();
			} else if (s.contains(X.get(i % N))) { // sが要素を含むあいだ、末尾から削除しつづける
				while (s.contains(X.get(i % N))) {
					s.remove(s.size() - 1);
				}
			} else {
				s.add(X.get(i % N));
			}
			
		}

		// 出力
		for (int i = 0; i < s.size(); i++) {
			System.out.print(s.get(i));
			System.out.print(i == s.size() - 1 ? "\n" : " ");
		}
	}
}