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;

int main(){
  int N;
  long long K;
  cin >> N >> K;
  
  vector<int> A(N), place(200001, -1), next(N, -1);
  for(int i = 0; i < N; i++){
    cin >> A[i];
    if(place[A[i]] >= 0){
      next[place[A[i]]] = i + 1;
    }
    place[A[i]] = i;
  }
  
  for(int i = 0; i < N; i++){
    if(next[place[A[i]]] == -1){
      next[place[A[i]]] = N + i + 1;
    }
  }
  
  long long turn = next[0];
  for(int i = next[0] % N; i != 0; i = next[i] % N){
    turn += next[i] - i;
  }
  
  turn *= K / (turn / N);
  
  for(int i = 0; turn + next[i] - i < K * N; i = next[i] % N){
    turn += next[i] - i;
  }
  
  for(int i = turn % N; i < N;){
    if(next[i] <= N) i = next[i];
    else{
      cout << A[i] << ' ';
      ++i;
    }
  }
  cout << endl;
  
  return 0;
}