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<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
const int N=2e5+5;
int n,m,top,a[N],fst[N],lst[N],nxt[N],vis[N],s[N];long long k;
int main(){
	scanf("%d%lld",&n,&k);
	for(int i=1;i<=n;++i){
		scanf("%d",&a[i]);
		if(!fst[a[i]])fst[a[i]]=i;
	}
	nxt[n+1]=1;
	for(int i=n;i;--i){
		if(!lst[a[i]])nxt[i]=fst[a[i]]+1;
		else nxt[i]=nxt[lst[a[i]]+1];
		lst[a[i]]=i;
	}
	for(int i=1;!vis[i];i=nxt[i])vis[s[++m]=i]=1;
	memset(vis,0,sizeof(vis));
	for(int i=s[(k-1)%m+1];i<=n;++i)
		if(!vis[a[i]])s[++top]=a[i],vis[a[i]]=1;
		else do vis[s[top--]]=0;while(s[top+1]!=a[i]);
	for(int i=1;i<=top;++i)printf("%d ",s[i]);
	return 0;
}
