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 <iostream>
#include <algorithm>
#include <iomanip>
#include <map>
#include <numeric>
#include <set>
#include <sstream>
#include <string>
#include <vector>
#include <queue>
#include <cassert>
using namespace std;
typedef long long ll;
const int INF = 1<<30;
const ll MOD = 1e9+7;
const double EPS = 1e-9;


int main(int argc, const char * argv[]) {
  ll N, K; cin >> N >> K;
  vector<int> A(N);
  for(int i=0; i<N; i++)
    cin >> A[i];
  
  vector<int> B(2*N);
  for(int i=0; i<2*N; i++)
    B[i] = A[i%N];
  
  vector<vector<int>> jump(300000);
  for(int i=0; i<2*N; i++)
    jump[B[i]].push_back(i);
  
  vector<int> next(N); // Aiからjumpしたときのindex
  for(int i=0; i<N; i++){
    auto it = upper_bound(jump[A[i]].begin(), jump[A[i]].end(), i);
    next[i] = (*it) + 1;
  }
  vector<int> start; // i個目Aをまたぐjumpにおける始点のindex
  int now;
  now = 0;
  while(true){
    if(next[now] > N) {
      start.push_back(now);
    }
    if(next[now]%N == 0) {
      start.push_back(now);
      break;
    }
    now = next[now]%N;
  }
  
  K %= (int)start.size();
  
  for(int i=start[K-1]; i<N; i++){
    if(next[i] <= N) i = next[i] - 1;
    else cout << A[i] << " ";
  }
  cout << endl;
  
  return 0;
}
