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>

#define MIN_INT -2147483648
#define MAX_INT 2147483647
#define MIN_LONG -9223372036854775808L
#define MAX_LONG 9223372036854775807L

#define long long long int

using namespace std;

// @author: pashka

int main() {
    ios::sync_with_stdio(false);

    int n;
    long k;
    cin >> n >> k;
    vector<int> a(n * 2);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        a[i + n] = a[i];
    }
    int MAX = 1000000;
    vector<int> last(MAX + 1);
    vector<int> next(n * 2);
    for (int i = a.size() - 1; i >= 0; i--) {
        next[i] = last[a[i]];
        last[a[i]] = i;
    }
    int x = 0;
    vector<long> pk(n, -1);
    while (true) {
        if (k <= 2) {
            vector<int> s;
            vector<bool> z(MAX + 1);
            for (int i = x; i < k * n; i++) {
                if (z[a[i % n]]) {
                    while (z[a[i % n]]) {
                        int t = s.back();
                        s.pop_back();
                        z[t] = false;
                    }
                } else {
                    z[a[i % n]] = true;
                    s.push_back(a[i % n]);
                }
            }
            for (int x : s) {
                cout << x << " ";
            }
            break;
        }
        x = next[x] + 1;
        while (x >= n) {
            k--;
            x -= n;
        }
        if (pk[x] != -1) {
            long d = pk[x] - k;
            k %= d;
        }
//        cout << x << " " << k << "\n";
        pk[x] = k;
    }

    return 0;
}