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 maxn=200003;
typedef long long ll;

int a[maxn],pos[maxn],nxt[maxn],val[maxn],fi[maxn];
int n;ll k;

int main(){
	scanf("%d%lld",&n,&k);
	for(int i=1;i<=n;++i)scanf("%d",&a[i]);
	if(n==1){
		if(k&1)printf("%d\n",a[1]);
		return 0;
	}
	for(int i=n;i>=1;--i)
		fi[a[i]]=i;
	for(int i=1;i<=n;++i){
		if(pos[a[i]])
			nxt[pos[a[i]]]=i%n+1;
		pos[a[i]]=i;
	}
	for(int i=1;i<=n;++i){
		if(!nxt[i]){
			if(fi[a[i]]==i)
				nxt[i]=i%n+1;
			else nxt[i]=fi[a[i]]+1;
		}
	}
	for(int i=1;i<=n;++i){
		if(nxt[i]>i+1)val[i]=nxt[i]-i;
		else val[i]=nxt[i]+n-i;
	}
	if(nxt[n]==1)val[n]=n+1;
	ll len=0;
	int cur=1;
	while(true){
		len+=val[cur];
		cur=nxt[cur];
		if(cur==1)break;
	}
	ll cir=len/n;
	k%=cir;
	if(!k)return 0;
	int id=1;cur=1;
	while(true){
		if(nxt[cur]>=cur+2){
			cur=nxt[cur];continue;
		}
		if(id==k){
			if(nxt[cur]==1&&cur!=n)return 0;
			printf("%d ",a[cur]);
			if(cur==n)return 0;
			++cur;
		}else{
			++id;
			cur=nxt[cur];
		}
	}
	return 0;
}

