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: Wrong Answer)

import java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long K = sc.nextLong();
		StringBuilder A = new StringBuilder();
		A.append(sc.next());
		Set<Integer> type = new HashSet<>();
		type.add(Character.getNumericValue(A.charAt(0)));
		for(int i = 1; i < N; i++) {
			String a = sc.next();
			if(a.charAt(0) == (A.charAt(A.length()-1)) )
				A.substring(A.length()-1);
			else {
				A.append(a);
				type.add(Integer.parseInt(a));
			}
		}
		int M = type.size();
		K %= (M+1);
		StringBuilder ans = new StringBuilder();
		Set<Integer> set = new HashSet<>();
		for(int i = 0; i < K; i++) {
			for(int j = 0; j < A.length(); j++) {
				if(set.contains(Character.getNumericValue((A.charAt(j))))) {
					int t = ans.indexOf(String.valueOf(A.charAt(j)));
					for(int k = t; k < ans.length(); k++)
						set.remove(Character.getNumericValue((ans.charAt(k))));
					ans.delete(t, ans.length());
				}
				else {
					set.add(Character.getNumericValue((A.charAt(j))));
					ans.append(A.charAt(j));
				}
			}
		}
		for(int i = 0; i < ans.length(); i++)
			System.out.print(ans.charAt(i)+ " ");
		System.out.println();

	}

}