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<set>
#include<map>
#include<stack>
#include<cmath>
#include<queue>
#include<cstdio>
#include<vector>
#include<climits>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#define LL long long
using namespace std;
LL read(){
	bool f=0;LL x=0;char c=getchar();
	while(c<'0'||'9'<c){if(c=='-')f=1;c=getchar();}
	while('0'<=c&&c<='9') x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return !f?x:-x;
}
#define MAXN 200000
#define INF 0x3f3f3f3f
bool vis[MAXN+5];
int n,a[MAXN+5],val[MAXN+5],nxt[MAXN+5];
void Print(int p){
	while(p<=n){
		if(nxt[p]>n) printf("%d ",a[p]),p++;
		else p=nxt[p]+1;
	}
	puts("");
	exit(0);
}
int main(){
	//freopen("dnd.in","r",stdin);
	//freopen("dnd.out","w",stdout);
	n=read();
	LL k=read();
	for(int i=1;i<=n;i++)
		a[i]=read();
	for(int i=2*n;i>=n+1;i--)
		val[a[i-n]]=i;
	for(int i=n;i>=1;i--)
		nxt[i]=val[a[i]],val[a[i]]=i;
	int p=1;
	LL sum=0;
	while(!vis[p]){
		sum+=nxt[p]-p,vis[p]=1;
		if(nxt[p]>n)
			p=(nxt[p]-n)%n+1;
		else p=nxt[p]%n+1;
	}
	k%=(sum/n+1);
	while(k){
		if(!k) break;
		if(k==1) Print(p);
		if(nxt[p]>=n){
			k--;
			if(nxt[p]==2*n) k--;
			p=(nxt[p]-n)%n+1;
		}
		else p=nxt[p]+1;
	}
	puts("");
	return 0;
}
