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 int long long
const int N=2e5+5;
int n,a[N],pos[N],nxt[N],cur=1;
vector<int> ans;
signed main(){
//	freopen("01-06.txt","r",stdin);
	int k;
	cin>>n>>k;
	for(int i=1;i<=n;++i)
		cin>>a[i];
	for(int i=n;i>=1;--i)
		pos[a[i]]=i;
	for(int i=n;i>=1;--i)
		nxt[i]=pos[a[i]],pos[a[i]]=i;
	int p=1;
	while(1){
		if(nxt[p]<=p) ++cur;
		p=nxt[p]+1;
		if(p==n+1){
			break;
		}
	}
	k%=cur;cur=0;p=1;
	while(1){
		if(nxt[p]<=p) ++cur;
		if(cur==k) break;
		p=nxt[p]+1;
	}
	while(1){
		if(nxt[p]<=p) ans.push_back(a[p]),p++;
		else p=nxt[p]+1;
		if(p==n+1) break;
	}
	for(auto v:ans) cout<<v<<" ";
	return 0;
}
