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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        // int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        //
        int n = Integer.parseInt(st.nextToken());
        long k = Long.parseLong(st.nextToken());
        st = new StringTokenizer(bf.readLine());
         int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
         int[] next = new int[n];
         int[] prev = new int[200001];
         Arrays.fill(prev, -1);
         for(int i=0; i<2*n; i++) {
            int j = i%n;
            if(prev[a[j]] != -1) {
              next[prev[a[j]]] = j;
            }
            prev[a[j]] = j;
         }
        // System.out.println(Arrays.toString(next));
         int count = 1; int pointer = 0;
         while(true) {
           int nextval = next[pointer];
           if(nextval <= pointer) count++;
           pointer = nextval + 1;
           //System.out.println(pointer);
           if(pointer == n) break;
         }
         k %= count;
         if(k == 0) {
           out.println();
           out.close();
           System.exit(0);
         }
         count = 1;
         pointer = 0;
         while(true) {
           int nextval = next[pointer];
           if(nextval <= pointer) {
             if(count == k) {
               StringBuilder sb = new StringBuilder();
               for(int i=pointer; i<n; i++) {
                 if(next[i] <= i) sb.append(a[i] + " ");
                 else i=next[i];
               }
               out.println(sb.toString());
               out.close(); System.exit(0);
             }
             count++;
           }
           pointer = nextval + 1;
           if(pointer == n) break;
         }
        out.close(); System.exit(0);
    }
}