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: Wrong Answer)

#include "bits/stdc++.h"
using namespace std;
typedef long long ll;

constexpr int MAXN = 2e5 + 42;

int val[MAXN], succ[MAXN], last[MAXN], pos[MAXN], in[MAXN];

int main() {
  int N;
  ll K;
  cin >> N >> K;
  for (int i = 0; i < N; i++) {
    cin >> val[i];
    last[val[i]] = i;
  }
  for (int i = 0; i < N; i++) {
    succ[last[val[i]]] = i;
    last[val[i]] = i;
  }

  int x = 0, t = 0;
  do {
    if (succ[x] <= x || succ[x] == N - 1) {
      pos[t++] = x;
    }
    x = (succ[x] + 1) % N;
  } while (x != 0);

  K = (K - 1) % t;

  vector<int> stk;
  for (int i = pos[K]; i < N; i++) {
    if (in[val[i]]) {
      while(stk.back() != val[i]) {
        in[stk.back()] = 0;
        stk.pop_back();
      }
      stk.pop_back();
    } else {
      stk.push_back(val[i]);
    }
    in[val[i]] ^= 1;
  }

  for (int i : stk) {
    cout << i << ' ';
  }
  cout << endl;

  return 0;
}