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
// by Balloons
#include <cstdio>
#include <cstring>
#include <vector>
#include <iostream>
#include <algorithm>
#define mpr make_pair
#define debug() puts("okkkkkkkk")
#define rep(i,a,b) for(int (i)=(a);(i)<=(b);(i)++)

using namespace std;

typedef long long LL;
#define int LL

const int inf = 1 << 30;
const int maxn=3e5+5; 

int n;
LL k;
int a[maxn],nxt[maxn];
int to[maxn][65];
__int128 st[maxn][65];

signed main(){
	scanf("%lld%lld",&n,&k);
	for(int i=0;i<n;i++)scanf("%lld",&a[i]);
	for(int i=n-1;i>=0;i--)nxt[a[i]]=n+i;
	for(int i=n-1;i>=0;i--){
		to[i][0]=nxt[a[i]]+1;
		st[i][0]=to[i][0]-i;
		to[i][0]=(to[i][0])%n;
		nxt[a[i]]=i;
	}
	
	for(int j=1;j<60;j++)
		for(int i=0;i<n;i++)
			to[i][j]=to[to[i][j-1]][j-1],
			st[i][j]=st[to[i][j-1]][j-1]+st[i][j-1];

	int p=0;LL pos=0;
	for(int j=59;j>=0;j--)
		if(pos+st[p][j]<=n*k)
			pos+=st[p][j], 
			p=to[p][j];
	
	vector<int>ans;
	while(pos<n*k){
		int cur=a[(pos)%n];
		if(pos+st[(pos)%n][0]>n*k){
			ans.push_back(cur);
			++ pos;
		} else pos+=st[(pos)%n][0];
	}
	for(int i=0;i<ans.size();i++)printf("%lld ",ans[i]);
	puts("");

	return 0;
}
