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;
#define modulo 1000000007
#define mod(mod_x) ((((long long)mod_x)+modulo)%modulo)
#define Inf 1000000000

int main(){
	int N;
	cin>>N;
	
	long long K;
	cin>>K;
	
	vector<int> A(N);
	for(int i=0;i<N;i++){
		cin>>A[i];
	}
	
	vector<int> last_ind(200001,-1);
	vector<int> next(N,-1);
	for(int i=0;i<N;i++){
		if(last_ind[A[i]]!=-1){
			next[last_ind[A[i]]] = i;
		}
		last_ind[A[i]] = i;
	}
	for(int i=0;i<N;i++){
		if(last_ind[A[i]]!=-1){
			next[last_ind[A[i]]] = i;
		}
		last_ind[A[i]] = i;
	}
	
	int shuuki = 1;
	int now = 0;
	while(true){
		int a = next[now];
		if(a<=now)shuuki++;
		if(a==N-1)break;
		now = a+1;
	}
	K--;
	K%=shuuki;
	
	now=0;
	if(K!=0){
		while(true){
			int a = next[now];
			if(a<=now){
				if(K==0)break;
				K--;
			}
			now = (a+1)%N;
		}
	}
	vector<int> ans(0);
	for(int i=now;i<N;i++){
		if(next[i]>i) i = next[i];
		else{
			ans.push_back(A[i]);
		}
	}
	for(int i=0;i<ans.size();i++){
		if(i!=0)cout<<' ';
		cout<<ans[i];
	}
	cout<<endl;

		
	
	
	return 0;
	
}