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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

unsigned long a[2 * 100000];
unsigned long pos = 0;

unsigned long adddata(unsigned long val)
{
    a[pos++] = val;

    for( unsigned long loop = 0; loop < pos - 1; loop ++ ) {
      if( a[loop] == val ) {
        pos = loop;
        break;
      }
    }

    return pos;
 }


int main(void)
{
  unsigned long n;
  unsigned long k;
  unsigned long v;
  unsigned long loop;
  
  scanf("%ld", &n);
  scanf("%ld", &k);
  
  for( loop = 0; loop < n; loop ++ ) {
	   scanf("%ld", &v);
       adddata(v);
  }

  if( k & 1 ) {
    if( pos <= 0 ) {
      printf( "\n");
    }
    else {
      for( loop = 0; loop < pos-1; loop ++ ) {
         printf( "%ld ", a[loop]);
      }
	    printf( "%ld\n", a[pos-1]);
    }
  }
  else {
    if( pos <= 1 ) {
      printf( "\n");
    }
    else {
      for( loop = 1; loop < pos-1; loop ++ ) {
         printf( "%ld ", a[loop]);
      }
	  printf( "%ld\n", a[pos-1]);
    }
  }
  
  
  return 0;
}