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;
using i64 = long long;
#define rep(i,s,e) for(i64 (i) = (s);(i) < (e);(i)++)
#define all(x) x.begin(),x.end()
#define let auto const

int main() {
  i64 N, K;
  cin >> N >> K;
  vector<i64> A(N);
  rep(i,0,N) cin >> A[i];
  vector<i64> next(N);
  map<i64, i64> mp;
  rep(i,0,N) {
    if(mp.count(A[i])) {
      i64 tmp = next[mp[A[i]]];
      next[mp[A[i]]] = i;
      next[i] = tmp;
      mp[A[i]] = i;
    }
    else {
      mp[A[i]] = i;
      next[i] = N + i;
    }
  }

  i64 cnt = 0;
  {
    i64 now = 0;
    while(true) {
      i64 ne = next[now];
      if(ne >= N) cnt++;
      now = (ne + 1) % N;
      if(now == 0) break;
    }
  }
  cnt++;
  K %= cnt;

  {
    cnt = 0;
    i64 now = 0;
    while(cnt < K - 1) {
      i64 ne = next[now];
      if(ne >= N) cnt++;
      now = (ne + 1) % N;
      if(now == 0) break;
    }
    vector<i64> vec;
    for(int i = now; i < N; i++) {
      if(next[i] >= N) {
        vec.push_back(A[i]);
      }
      else i = next[i];
    }

    for(int i = 0;i < vec.size();i++) {
      cout << vec[i] << " \n"[i +1 == vec.size()];
    }
  }
}
