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.

Examples

Input

3 2
1 2 3


Output

2 3


Input

5 10
1 2 3 2 3


Output

3


Input

6 1000000000000
1 1 2 2 3 3


Output




Input

11 97
3 1 4 1 5 9 2 6 5 3 5


Output

9 2 6
#include <bits/stdc++.h>
using namespace std;

const int N = 200005;
const int LK = 42;

int n;
long long k;
int a[N];

int first[N];
int lst[N];
int nxt[N];

int sp[LK][N];

int main() {
  memset(first, -1, sizeof first);
  memset(nxt, -1, sizeof nxt);
  
  scanf("%d %lld", &n, &k);
  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
    
    if (first[a[i]] == -1) first[a[i]] = i;
    else {
      nxt[lst[a[i]]] = i + 1;
    }
    
    lst[a[i]] = i;
  }
  
  sp[0][n] = 0;
  for (int i = n-1; i >= 0; --i) {
    if (nxt[i] == -1) sp[0][i] = first[a[i]] + 1;
    else sp[0][i] = sp[0][nxt[i]];
  }
  
  for (int i = 1; i < LK; ++i) for (int j = 0; j <= n; ++j) sp[i][j] = sp[i-1][sp[i-1][j]];
  
  --k;
  int cur = 0;
  while (k > 0) {
    int ctz = __builtin_ctzll(k);
    k -= 1LL << ctz;

    cur = sp[ctz][cur];
  }
  
  bool space = false;
  for (; cur < n;) {
    if (nxt[cur] != -1) cur = nxt[cur];
    else {
      if (space) printf(" ");
      space = true;

      printf("%d", a[cur++]);
    }
  }
  printf("\n");
  
  return 0;
}
