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++)

using namespace std;
using lint=long long;

int main(){
	int n;
	lint k; scanf("%d%lld",&n,&k);
	vector<int> a(n);
	rep(i,n) scanf("%d",&a[i]);

	vector<int> next(n);
	{
		vector<vector<int>> Pos(2e5+1);
		rep(i,n) Pos[a[i]].emplace_back(i);
		rep(x,2e5+1) rep(i,Pos[x].size()) next[Pos[x][i]]=Pos[x][(i+1)%Pos[x].size()];
	}

	int per=1;
	{
		int p=0;
		do{
			if(p>=next[p]) per++;
			p=(next[p]+1)%n;
		}while(p!=0);
	}

	if(k%per==0) return 0;

	k=(k-1)%per;

	int p=0;
	while(k>0){
		if(p>=next[p]) k--;
		p=(next[p]+1)%n;
	}

	vector<int> ans;
	while(p<n){
		if(p>=next[p]) ans.emplace_back(a[p]), p++;
		else           p=next[p]+1;
	}
	rep(i,ans.size()) printf("%d%c",ans[i],i+1<ans.size()?' ':'\n');

	return 0;
}
