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 N=400002;
typedef long long ll;
int n,a[N*5],v[N],top,st[N],las[N],ne[N],i,sum,j;
bool vis[N];
ll k;
int main(){
	scanf("%d%lld",&n,&k);
	for (i=0;i<n;i++) scanf("%d",&a[i]);
	for (j=1;j<3;j++)
		for (i=0;i<n;i++) a[n*j+i]=a[i];
	for (i=2*n-1;i>=0;i--){
		if (i<n){
			ne[i]=las[a[i]]+1;
			v[i]=ne[i]/n,ne[i]%=n;
		}
		las[a[i]]=i;
	}
	for (i=ne[0],sum=v[0];i;sum+=v[i],i=ne[i]);
	k%=sum;
	for (i=0;k>=3;k-=v[i],i=ne[i]);
	for (;i<k*n;i++){
		if (vis[a[i]]){
			for (;top && st[top]!=a[i];vis[st[top]]=0,top--);
			top--,vis[a[i]]=0;
		}else vis[a[i]]=1,st[++top]=a[i];
	}
	for (i=1;i<=top;i++) printf("%d ",st[i]);
}