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
map < int , int > now;
int arr[200003] , nxt[200003] , len[200003] , N , K;
int tms[200003];

signed main(){
	cin >> N >> K;
	for(int i = 0 ; i < N ; ++i) cin >> arr[i];
	for(int i = N - 1 ; i >= 0 ; --i){
		if(now.find(arr[i]) != now.end()) nxt[i] = now[arr[i]];
		now[arr[i]] = i;
	}
	for(int i = N - 1 ; i >= 0 ; --i)
		if(!nxt[i]) nxt[i] = N + now[arr[i]];
	int cnt = 0 , all = N * K;
	while(!len[cnt % N]){len[cnt % N] = cnt + 1; cnt += nxt[cnt % N] - (cnt % N) + 1;}
	if(all > len[cnt % N] - 1){
		all -= len[cnt % N] - 1;
		all = all % (cnt / N * N);
		cnt %= N;
	}
	else cnt = 0;
	while(all >= nxt[cnt] - cnt + 1){
		all -= nxt[cnt] - cnt + 1;
		cnt = (nxt[cnt] + 1) % N;
	}
	deque < int > q;
	while(all){
		if(tms[arr[cnt]])
			while(tms[arr[cnt]]){
				--tms[q.back()]; q.pop_back();
			}
		else{q.push_back(arr[cnt]); ++tms[arr[cnt]];}
		--all; cnt = (cnt + 1) % N;
	}
	while(!q.empty()){
		printf("%lld " , q.front()); q.pop_front();
	}
	return 0;
}
