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 ll = long long;

int main() {
  ll n, k;
  cin >> n >> k;
  vector<int> a(n);
  for (auto& e : a) cin >> e;

  vector<int> t(n, -1);
  {
    vector<int> u(2e5 + 1, -1);
    for (int _ = 0; _ < 2; _++) {
      for (int i = n - 1; i >= 0; i--) {
        if (t[i] == -1 && u[a[i]] != -1) t[i] = u[a[i]];
        u[a[i]] = i;
      }
    }
  }

  vector<int> r;
  vector<int> v(n, -1);
  for (ll i = 0, j = 0; i < k; j++, i += j / n, j %= n) {
    if (v[j] != -1 && i + (i - v[j]) < k) i += (k - i - 1) / (i - v[j]) * (i - v[j]);
    v[j] = i;

    if (j < t[j]) {
      j = t[j];
    } else if (i + 1 < k) {
      i++;
      j = t[j];
    } else {
      r.push_back(a[j]);
    }
  }

  for (auto e : r) cout << e << ' ';
  cout << endl;
}
