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
/*Lucky_Glass*/
#include<stack>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int N=2e5;

int n,Ia[N+3],Elas[N+3],Enxt[N+3],Elen[N+3],Ecnt[N+3],Estk[N+3];
long long Ik,Evis[N+3];

int main(){
	scanf("%d%lld",&n,&Ik);
	for(int i=1;i<=n;i++)
		scanf("%d",&Ia[i]);
	for(int i=n;i>=1;i--){
		if(Elas[Ia[i]]){
			Enxt[i]=Elas[Ia[i]]+1;
			if(Enxt[i]>n) Enxt[i]-=n;
			Elen[i]=Elas[Ia[i]]+1-i;
		}
		Elas[Ia[i]]=i;
	}
	for(int i=n;i>=1;i--)
		if(Enxt[i]==0){
			Enxt[i]=Elas[Ia[i]]+1;
			if(Enxt[i]>n) Enxt[i]-=n;
			Elen[i]=n+Elas[Ia[i]]+1-i;
		}
	int u=1;
	long long Ncnt=0,Ncir;
	memset(Evis,-1,sizeof Evis);
	while(true){
		if(Evis[u]!=-1){
			Ncir=Ncnt-Evis[u];
			break;
		}
		Evis[u]=Ncnt;
		Ncnt+=Elen[u];
		u=Enxt[u];
	}
	Ik*=n;
	Ik%=Ncir;
	u=1;
	while(true){
		if(Ik<Elen[u]){
			int Vtop=0;
			for(int i=0;i<Ik;i++){
				int v=i+u;
				while(v>n) v-=n;
				if(Ecnt[Ia[v]]){
					while(Ecnt[Ia[v]]){
						Ecnt[Estk[Vtop]]--;
						Estk[Vtop--]=0;
					}
				}
				else{
					Ecnt[Ia[v]]++;
					Estk[++Vtop]=Ia[v];
				}
			}
			for(int i=1;i<=Vtop;i++){
				if(i>1) printf(" ");
				printf("%d",Estk[i]);
			}
			printf("\n");
			break;
		}
		Ik-=Elen[u];
		u=Enxt[u];
	}
	return 0;
}