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;

#define REP(i,n) for(int i = 0; i < (int)(n); i++)
#define ALL(a) (a).begin(), (a).end()

int main(){
  int n;
  uint64_t k;
  cin >> n >> k;
  vector<int> a(n);
  REP(i, n){
    cin >> a[i];
  }
  vector<int> j(n, -1);
  vector<int> l(200020, -1);
  REP(i, n){
    int x = a[i];
    if(l[x] >= 0){
      j[l[x]] = i + 1;
    }
    l[x] = i;
  }
  REP(i, n){
    int x = a[i];
    if(l[x] >= 0){
      j[l[x]] = n + i + 1;
      l[x] = -1;
    }
  }
  int p = 0;
  int q = 0;
  do{
    p = j[p];
    q += p / n;
    p %= n;
  }while(p != 0);
  k %= q;
  if(k == 0){
    cout << endl;
    return 0;
  }
  q = 0;
  while(1){
    int np = j[p];
    if(np >= n){
      q += 1;
      if(q == k) break;
      np -= n;
    }
    p = np;
  }
  bool first = true;
  while(p < n){
    if(j[p] <= n){
      p = j[p];
    }else{
      if(!first) putchar(32);
      printf("%d", a[p]);
      first = false;
      ++p;
    }
  }
  puts("");
  return 0;
}
