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;
const int maxn=2e5+5;
typedef long long ll;
int n;
ll k;
int a[maxn];
int fir[maxn];
int lst[maxn];
int nxt[maxn];
int v[maxn];
int s[maxn];
int cnt;
int top;
int main(){
	scanf("%d%lld",&n,&k);
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
		if(!fir[a[i]]) fir[a[i]]=i;
	} 
	nxt[n+1]=1;
	for(int i=n;i>=1;i--){
		if(!lst[a[i]]) nxt[i]=fir[a[i]]+1;
		else nxt[i]=nxt[lst[a[i]]+1];
		lst[a[i]]=i;
	}
	for(int i=1;!v[i];i=nxt[i]) v[i]=1,s[++cnt]=i;
	memset(v,0,sizeof(v));
	for(int i=s[(k-1)%cnt+1];i<=n;i++)
		if(!v[a[i]]){
			s[++top]=a[i];
			v[a[i]]=1;
		}else{
			do{
				v[s[top]]=0;
				top--;
			}while(s[top+1]!=a[i]);
		}
	for(int i=1;i<=top;i++) printf("%d ",s[i]);
	printf("\n");
	return 0; 
} 