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<cmath>
#define ll long long
using namespace std;
int n;
int a[1000010],nx[1000010],last[1000010],pos[1000010];
ll k;
int main(){
	scanf("%d%lld",&n,&k);
	for(register int i=1;i<=n;i++)scanf("%d",&a[i]);
	for(register int i=1;i<=n;i++){
		nx[last[a[i]]]=i;
		last[a[i]]=i;
	}
	for(register int i=1;i<=n;i++){
		if(!nx[last[a[i]]])nx[last[a[i]]]=i;
		last[a[i]]=i;
	}
	int now=0,cnt=1;
	while(now!=n){
		now++;
		if(!pos[cnt])pos[cnt]=now;
		if(nx[now]<=now)cnt++;
		now=nx[now];
	}
	k=k%(1ll*cnt);
	now=pos[(int)k];
	while(now&&now<=n){
		while(nx[now]>now)now=nx[now]+1;
		if(now>n)break;
		cout<<a[now]<<" ";
		now++;
	}
	return 0;
}