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<stack>
#include<cstdio>
#include<algorithm>
using namespace std;
#define LL long long
const int MAXN=400005;
int N,A[MAXN],P;
int vis[MAXN];
int V[MAXN],R[MAXN];
long long K,Ans,Sum;
void Print(int p){
	for(int i=p;i<=N;i++){
		if(R[i]<=N)i=R[i];
		else printf("%d ",A[i]);
	}puts("");
}
void Solve(){
	//Ans++;
	if(K==0)return ;
	if(K==1){Print(P);return ;}
	if(R[P]>=N){K--;
		if(R[P]==2*N)K--;
		P=(R[P]-N)%N+1;
	}
	else P=R[P]+1;
	Solve();
}
int main(){
	//freopen("dnd.in","r",stdin);
	//freopen("dnd.out","w",stdout);
	scanf("%d%lld",&N,&K);
	for(int i=1;i<=N;i++)
		scanf("%d",&A[i]);
	for(int i=2*N;i>=N+1;i--)V[A[i-N]]=i;
	for(int i=N;i>=1;i--)R[i]=V[A[i]],V[A[i]]=i;
	int p=1;
	while(!vis[p]){
		vis[p]=1;Sum+=R[p]-p;
		if(R[p]>N)p=(R[p]-N)%N+1;
		else p=R[p]%N+1;
	}Sum=Sum/N+1;K%=Sum;
	P=p;Solve();
	//printf("%lld\n",Ans);
}

