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>
#define rep(i,n)for(int i=0;i<(n);i++)
#define MOD 1000000007
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3f
#define EPS (1e-10)
using namespace std;
typedef long long ll;

int a[500000];
int nx[40][500000];
ll cnt[40][500000];

int main(){
	int n;ll K;cin>>n>>K;
	rep(i,n){
		scanf("%d",&a[i]);
		a[i+n]=a[i];
	}
	map<int,int>mp;
	for(int i=2*n-1;i>=0;i--){
		nx[0][i]=(mp[a[i]]+1)%n;
		cnt[0][i]=mp[a[i]]+1-i;
		mp[a[i]]=i;
	}
	for(int i=1;i<40;i++){
		rep(j,n){
			nx[i][j]=nx[i-1][nx[i-1][j]];
			cnt[i][j]=cnt[i-1][j]+cnt[i-1][nx[i-1][j]];
		}
	}
	ll sum=n*K;
	sum--;
	int pos=0;
	for(int i=39;i>=0;i--){
		while(sum>=cnt[i][pos]){
			sum-=cnt[i][pos];
			pos=nx[i][pos];
		}
	}
	mp.clear();
	int cur=pos;
	stack<int>st;
	rep(i,sum+1){
		if(mp[a[cur]]){
			while(mp[a[cur]]){
				mp[st.top()]--;
				st.pop();
			}
		}
		else{
			st.push(a[cur]);
			mp[st.top()]++;
		}
		cur=(cur+1)%n;
	}
	vector<int>ans;
	while(!st.empty()){
		ans.push_back(st.top());
		st.pop();
	}
	reverse(ans.begin(),ans.end());
	for(int i:ans){
		printf("%d ",i);
	}
	puts("");
}