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 n, a[200200], order[200200];
long long k;
vector<int> id[200200];

int getMove(long long step)
{
  int curId = step % n, val = a[curId], curOrder = order[curId];
  if (curOrder + 1 == id[val].size())
    return id[val][0] + n - curId;
  return id[val][curOrder + 1] - curId;
}

void solve(long long from, long long to)
{
  long long step = from;
  while (step < to)
  {
    int move = getMove(step);
    if (step + move < to) step = step + move + 1;
    else
    {
      cout << a[step % n] << ' ';
      step++;
    }
  }
  cout << endl;
  exit(0);
}

int main()
{
  ios_base::sync_with_stdio(0);
  cin.tie(0);


  cin >> n >> k;
  for (int i = 0; i < n; i++)
  {
    cin >> a[i];
    order[i] = id[a[i]].size();
    id[a[i]].push_back(i);
  }

  vector<int> seen(n, -1);
  long long step = 0;
  while (step < k * n)
  {
    seen[step % n] = step;
    int move = getMove(step);
    if (step + move + 1 >= k * n) solve(step, k * n);
    else
    {
      step += move + 1;
      if (seen[step % n] >= 0)
      {
        long long  cycle = step - seen[step % n], startCycle = seen[step % n];
        solve(startCycle, startCycle + (k * n - startCycle) % cycle);
      }
    }
  }
}
