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;
typedef long long ll;
const ll MOD = 1e9 + 7;
const ll INF = 1LL << 60;
int A[400000];
ll d[61][200000];
int pos[200001];
int main() {
	ll N, K;
	cin >> N >> K;
	for (int i = 0; i < N; i++) {
		cin >> A[i];
		A[i + N] = A[i];
	}
	for (int i = 2 * N - 1; i >= 0; i--) {
		if (i < N) d[0][i] = pos[A[i]] - i + 1;
		pos[A[i]] = i;
	}
	for (int i = 1; i <=  60; i++) {
		for (int j = 0; j < N; j++) {
			d[i][j] = min(INF, d[i - 1][j] + d[i - 1][(j + d[i - 1][j]) % N]);
		}
	}
	ll now = 0;
	for (int i = 60; i >= 0; i--) {
		if (now + d[i][now%N] <= N * K) now += d[i][now%N];
	}
	deque<int> q;
	set<int> S;
	for (ll i = now; i < N*K; i++) {
		if (S.count(A[i%N])) {
			while (q.back() != A[i%N]) {
				S.erase(q.back());
				q.pop_back();
			}
			S.erase(A[i%N]);
			q.pop_back();
		}
		else {
			S.insert(A[i%N]);
			q.push_back(A[i%N]);
		}
	}
	for (int i = 0; i < q.size(); i++) cout << q[i] << " ";
	cout << endl;
}