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 <iostream>
#include <cstring>
#include <algorithm>
#define ll long long
using namespace std;
template <class T>
inline void rd(T &x) {
	x=0; char c=getchar(); int f=1;
	while(!isdigit(c)) { if(c=='-') f=-1; c=getchar(); }
	while(isdigit(c)) x=x*10-'0'+c,c=getchar(); x*=f;
}
const int N=2e5+10;
int head[N],nxt[N<<1],n,a[N];
int vis[N],ex[N];
ll K;
int stk[N],top;
int main() {
	 rd(n),rd(K);
	 for(int i=0;i<n;++i) rd(a[i]);
	 for(int i=n-1;i>=0;--i) head[a[i]]=n+i;
	 for(int i=n-1;i>=0;--i) {
	 	nxt[i]=head[a[i]];
	 	head[a[i]]=i;
	}
	memset(vis,-1,sizeof(vis));
	int cnt=0,cur=0;
	vis[cur]=cnt;
	while(true) {
		cur=nxt[cur]+1;
		cnt+=cur/n,cur%=n;
		if(vis[cur]!=-1) {
			break;
		}
		vis[cur]=cnt;
	}
//	cout<<cur<<' '<<vis[cur]<<' '<<cnt<<endl;
	K-=vis[cur];
	K%=cnt-vis[cur];
	cnt=0;
//	cout<<K<<endl;
	while(true) {
		int v=nxt[cur]+1;
		int cnt1=cnt+v/n;
		if(cnt1>=K) break;
		cur=v%n,cnt=cnt1;
//		cout<<cur<<'-'<<cnt<<endl;
	}
//	cout<<cur<<' '<<cnt<<endl;
	for(int j=cnt+1;j<=K;++j) {
		for(int i=(j==cnt+1)?cur:0;i<n;++i) {
			if(ex[a[i]]) {
				do ex[stk[top]]=0;
				while(stk[top--]!=a[i]);
			}
			else ex[stk[++top]=a[i]]=1;
		}
	}
	for(int i=1;i<=top;++i) printf("%d ",stk[i]);
	return 0;
}