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 <iostream>
#include <string>
#include <vector>
#include <unordered_map>
#include <algorithm>

using namespace std;
using ll = long long;

int main(){
	ios_base::sync_with_stdio(false);
	int n;
	ll k;
	cin >> n >> k;
	vector<int> a(n);
	for(int i = 0; i < n; ++i){ cin >> a[i]; }
	const int m = *std::max_element(a.begin(), a.end()) + 1;

	vector<int> last(m);
	for(int i = n - 1; i >= 0; --i){ last[a[i]] = i; }

	vector<int> next(n);
	for(int i = n - 1; i >= 0; --i){
		next[i] = last[a[i]];
		last[a[i]] = i;
	}

	vector<int> heads;
	heads.push_back(0);
	do {
		int cur = heads.back();
		while(true){
			if(next[cur] == n - 1){
				if(next[cur] == cur){ heads.push_back(n); }
				heads.push_back(0);
				break;
			}else if(next[cur] <= cur){
				heads.push_back(next[cur] + 1);
				break;
			}else{
				cur = next[cur] + 1;
			}
		}
	} while(heads.back() != 0);
	heads.pop_back();

	vector<int> b;
	for(int i = heads[(k - 1) % heads.size()]; i < n; ++i){
		if(next[i] > i){
			i = next[i];
		}else{
			b.push_back(a[i]);
		}
	}
	for(const auto x : b){
		cout << x << " ";
	}
	cout << endl;
	return 0;
}

