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<vector>
#define move move1
#define int long long
using namespace std;
const int N=4e5+2;
const int inf=1e18;
vector<int> lis[N],damn;
int ar[N],move[N][65];
bool cnt[N];
signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n,i,j,k=0,l=0,num;
	cin>>n>>num;
	for(i=0;i<n;i++){
		cin>>ar[i];
		lis[ar[i]].push_back(i);		
	}
	for(i=1;i<=2e5;i++){
		for(j=0;j<lis[i].size();j++){
			if(j==lis[i].size()-1){
				move[lis[i][j]][0]=lis[i][0]+n-lis[i][j]+1;
			}
			else{
				move[lis[i][j]][0]=lis[i][j+1]-lis[i][j]+1;
			}
		}
	}
	for(i=1;i<=60;i++){
		for(j=0;j<n;j++){
			move[j][i]=move[j][i-1]+move[(j+move[j][i-1])%n][i-1];
			if(move[j][i]>inf){
				move[j][i]=inf;
			}
		}
	}
	for(i=60;i>=0;i--){
		if(k+move[k%n][i]<num*n){
			k+=move[k%n][i];
		}
	}
	k%=n;
	for(i=k;i<n;i++){
		if(!cnt[ar[i]]){
			cnt[ar[i]]=true;
			damn.push_back(ar[i]);
		}
		else{
			while(true){
				j=damn.back();
				cnt[j]=false;
				damn.pop_back();
				if(j==ar[i]){
					break;
				}
			}
		}
	}
	for(i=0;i<damn.size();i++){
		cout<<damn[i]<<' ';
	}
}