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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int N = scn.nextInt();
		long K = scn.nextLong();
		Number[] A = new Number[N];

		int[] first = new int[N + 1];
		int[] last = new int[N + 1];
		Arrays.fill(first, -1);
		Arrays.fill(last, -1);

		for (int i = 0; i < N; i++) {
			int a = scn.nextInt();
			if (first[a] == -1)
				first[a] = i;
			if (last[a] != -1) {
				A[last[a]].setNext(i);
			}
			A[i] = new Number(a);
			last[a] = i;
		}
		ArrayList<ArrayList<Integer>> ans = new ArrayList<ArrayList<Integer>>();
		ArrayList<Integer> buf = new ArrayList<Integer>();
		do {
			ans.add(buf);
			int start;
			if(buf.isEmpty()) {
				start = 0;
			}else {
				start = first[buf.get(0)]+1;
			}
			buf = new ArrayList<Integer>();
			for(;start < N;start++) {
				Number a = A[start];
				if(a.next==-1) {
					buf.add(a.value);
				}else {
					start = a.next;
				}
			}
		} while (!buf.isEmpty());

		ArrayList<Integer> real_ans = ans.get((int)(K%(ans.size())));

		for(int i = 0;i < real_ans.size();i++) {
			System.out.print(((i==0)?"":" ")+real_ans.get(i));
		}
		if(real_ans.size()==0) {
			System.out.println("");
		}


	}

}

class Number {
	int value;
	int next;

	public Number(int value) {
		this.value = value;
		this.next = -1;
	}

	public void setNext(int next) {
		this.next = next;
	}

}