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 PII = pair<int, int>;
#define F first
#define S second
constexpr int maxn = 2e5 * 2 + 10;
int64_t k;
int n, a[maxn], f[maxn], g[maxn];

int main() {
  scanf("%d%lld", &n, &k);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
    a[i + n] = a[i];
  }
  unordered_map<int, int> m;
  for (int i = n * 2; i >= 1; --i) {
    if (m.count(a[i])) {
      f[i] = m[a[i]] + 1;
    } else {
      f[i] = i;
    }
    m[a[i]] = i;
  }
  f[n * 2 + 1] = n * 2 + 1;
  for (int i = n * 2 + 1; i >= 1; --i) {
    g[i] = i == f[i] ? f[i] : g[f[i]];
  }
  int s = n + 1;
  m.clear();
  int cnt = 0;
  while (k-- > 0) {
    s = g[s] - n;
    cnt++;
    if (m.count(s)) {
      int len = cnt - m[s];
      k %= len;
    }
    m[s] = cnt;
  }
  unordered_set<int> vis;
  vector<int> st;
  for (int i = s; i <= n; ++i) {
    if (vis.count(a[i])) {
      while (st.back() != a[i]) {
        vis.erase(st.back());
        st.pop_back();
      }
      vis.erase(st.back());
      st.pop_back();
    } else{
      vis.insert(a[i]);
      st.push_back(a[i]);
    }
  }
  for (size_t i = 0; i < st.size(); ++i)
    printf("%d%c", st[i], " \n"[i + 1 == st.size()]);
  return 0;
}

