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;

#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
#define mp make_pair
#define pb push_back
#define fst first
#define snd second
typedef long long ll;
typedef pair<int,int> pii;

const int maxn=200005;
int n;
ll k;
int a[maxn];
vector<int>pos[maxn];

int main(){
	scanf("%d%lld",&n,&k);
	REP(i,n)scanf("%d",&a[i]),pos[a[i]].pb(i);
	int cur=1,len=1;
	for(;;){
		int nxt=upper_bound(pos[a[cur]].begin(),pos[a[cur]].end(),cur)-pos[a[cur]].begin();
		if(nxt==pos[a[cur]].size())nxt=0,len++;
		if(pos[a[cur]][nxt]==n)break;
		cur=pos[a[cur]][nxt]+1;
	}
	k%=len;
	if(k==0){
		puts("");
		return 0;
	} 
	cur=1;len=1;
	while(cur<=n){
		int nxt=upper_bound(pos[a[cur]].begin(),pos[a[cur]].end(),cur)-pos[a[cur]].begin();
		if(nxt==pos[a[cur]].size()){
			if(len==k)printf("%d ",a[cur]),cur++;
			else cur=pos[a[cur]][0]+1,len++;
		}
		else cur=pos[a[cur]][nxt]+1;
	}
	puts("");
	return 0;
} 