Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3 2
1 2 3

Sample Output 1

2 3

In this case, X=(1,2,3,1,2,3).
We will perform the operations as follows:

i=0: s does not contain 1, so we add 1 to the end of s, resulting in s=(1).

i=1: s does not contain 2, so we add 2 to the end of s, resulting in s=(1,2).

i=2: s does not contain 3, so we add 3 to the end of s, resulting in s=(1,2,3).

i=3: s does contain 1, so we repeatedly delete the element at the end of s as long as s contains 1, which causes the following changes to s: (1,2,3)→(1,2)→(1)→().

i=4: s does not contain 2, so we add 2 to the end of s, resulting in s=(2).

i=5: s does not contain 3, so we add 3 to the end of s, resulting in s=(2,3).

Sample Input 2

5 10
1 2 3 2 3

Sample Output 2

3

Sample Input 3

6 1000000000000
1 1 2 2 3 3

Sample Output 3

s may be empty in the end.

Sample Input 4

11 97
3 1 4 1 5 9 2 6 5 3 5

Sample Output 4

9 2 6

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ul;
typedef signed long long ll;

mt19937 mt(time(nullptr));
// uniform_int_distribution< int > rand_int(0, 10) // rand[0, 10] inclusive

int main(void)
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed;
  ll n, k;
  cin >> n >> k;
  vector< ll > a(n);
  for (ll i=0; i<n; ++i) cin >> a[i];
  unordered_map< ll, ll > near;
  vector< ll > cstartidx(n+1, n);
  //cstartidx[n-1] = n-1;
  //near[a[n-1]] = n-1;
  for (ll i=n-1; i>=0; --i) {
    if (near.count(a[i]) > 0) {
      cstartidx[i] = cstartidx[near[a[i]]+1];
    } else cstartidx[i] = i;
    //cerr << cstartidx[i] << " ";
    near[a[i]] = i;
  }
  //cerr << endl;
  vector< ll > nstartidx(n);
  for (ll i=0; i<n; ++i) {
    if (cstartidx[i]==n) nstartidx[i] = n;
    else nstartidx[i] = (cstartidx[near[a[cstartidx[i]]]+1]);
    //cerr << nstartidx[i] << " ";
  }
  //cerr << endl;
  ul start = 0;
  vector< ll > v(n+1, -1);
  bool l_flg = false;
  for (ll i=0; i<k-1; ++i) {
    if (start == n) {
      k -= (k-2-i)/(i+1)*(i+1);
      start = 0;
      continue;
    }
    v[start] = i;
    /*
    if (!l_flg)
      cerr << i << " " << start << endl;
      */
    start = nstartidx[start];
    if (!l_flg) {
      if (v[start] >= 0) {
        l_flg = true;
        k -= (k-2-i)/(i+1-v[start])*(i+1-v[start]);
        //cerr << start << ":" << v[start] << " " << i << endl;
      }
    }
  }
  vector< ll > s;
  unordered_map< ll, ll > cnt;
  for (ll i=start; i<n; ++i) {
    if (cnt.count(a[i]) == 0 || cnt[a[i]] == 0) {
      s.push_back(a[i]);
      cnt[a[i]] = 1;
    } else {
      while (cnt[a[i]] > 0) {
        cnt[s[s.size()-1]]--;
        s.pop_back();
      }
    }
  }
  if (s.size() == 0) return 0;
  for (ll i=0; i<s.size(); ++i) cout << s[i] << " ";
  cout << endl;
  return 0;
}