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>

template <size_t N, typename T, typename U = T, std::enable_if_t<
  N == 1, std::nullptr_t> = nullptr>
auto make_vector(size_t sz, T t) {
  return std::vector<U>(sz, t);
}
template <size_t N, typename T, std::enable_if_t<
  N == 1, std::nullptr_t> = nullptr>
auto make_vector(size_t sz) {
  return std::vector<T>(sz);
}
template <size_t N, typename T, typename... Args, std::enable_if_t<
  N != 1, std::nullptr_t> = nullptr>
auto make_vector(size_t a, Args... args) {
  return make_vector<1>(a, make_vector<N - 1, T>(args...));
}
template <typename T, typename Size_t>
auto& at(T& t, Size_t i) {
  return t.at(i);
}
template <typename T, typename Size_t, typename... Args>
auto& at(T& t, Size_t i, Args... args) {
  return at(t.at(i), args...);
}

int main() {
  std::cin.tie(0); std::cin.sync_with_stdio(false);
  int n; long long k; std::cin >> n >> k;
  std::vector<int> a(n);
  for (auto& x : a) {std::cin >> x; x--;}
  constexpr int max = 2e5;
  auto m = make_vector<2, int>(max, 0);
  for (int i = 0; i < n; i++) {
    m.at(a.at(i)).push_back(i);
  }
  auto add = std::vector<int>(n);
  for (auto& v : m) {
    if (v.empty()) continue;
    int sz = v.size();
    v.push_back(n + v.front());
    for (int i = 0; i < sz; i++) {
      auto crr = v.at(i), nxt = v.at(i + 1);
      assert(0 <= crr && crr < n && crr < nxt);
      add.at(crr) = nxt - crr + 1;
    }
  }
  auto moved = [&] (auto x) {
    return x + add.at(x % n);
  };
  k %= [&] {
    long long ret = 0;
    for (int i = 0; i < n; i++) {
      ret = moved(ret);
      if (ret % n == 0) break;
    }
    assert(ret % n == 0);
    return ret / n;
  }();
  long long crr = 0, goal = n * k;
  std::vector<int> ans;
  while (crr < goal) {
    auto nxt = moved(crr);
    if (nxt <= goal) {
      crr = nxt;
      continue;
    }
    ans.push_back(a.at((crr++ % n)));
  }
  int sz = ans.size();
  for (int i = 0; i < sz; i++) {
    std::cout << (i > 0 ? " " : "") << ans.at(i) + 1;
  }
  std::cout << std::endl;
  return 0;
}