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 <iostream>
#include <cstdio>
#include <string.h>
#include <cstdlib>
#define N 200005
using namespace std;
typedef long long ll;
int n,a[N],L[N],R[N],nxt[N];
ll K;
bool vis[N];
int dis(int x,int y){
	if(y==1&&x==n) return n+1;
	return y>x+1?y-x:y+n-x;
}
int ans[N];
void sim(int pos,int res){
    memset(L,0,sizeof(L));
    int len=0;
    for(int i=1;i<=res;i++,pos=pos==n?1:pos+1){
        if(L[a[pos]]){
            while(ans[len]!=a[pos]) L[ans[len--]]=0;
            --len;
            L[a[pos]]=0;
            continue;
        }
        ans[++len]=a[pos];
        L[a[pos]]=len;
    }
    for(int i=1;i<=len;i++) printf("%d ",ans[i]);
}
int main(){
	scanf("%d%lld",&n,&K);
	K*=n;
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	for(int i=1;i<=n;i++) if(!L[a[i]]) L[a[i]]=i;
	for(int i=n;i;i--){
		if(R[a[i]]) nxt[i]=R[a[i]]+1<=n?R[a[i]]+1:1;
		else nxt[i]=L[a[i]]+1<=n?L[a[i]]+1:1;
		R[a[i]]=i;
	}
	int x=1;
	while(!vis[x]){
		vis[x]=1;
		if(K<=n){
			sim(x,K);
			return 0;
		}
		K-=dis(x,nxt[x]);
		x=nxt[x];
	}
	ll sum=0;
	memset(vis,0,sizeof(vis));
	while(!vis[x]){
		vis[x]=1;
		sum+=dis(x,nxt[x]);
		x=nxt[x];
	}
	K%=sum;
	while(K>=dis(x,nxt[x])){
		K-=dis(x,nxt[x]);
		x=nxt[x];
	}
	sim(x,K);
	return 0;
}
