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 rep(i,x,y) for(int i=x;i<y;i++)
#define print(A,x,n) rep(I,0,n){cout<<(I ? " ":"")<<A[I]x;}cout<<endl;
#define pprint(A,y,m,n) rep(J,0,m){print(A[J],y,n);}
const long mod=998244353;
const int size=2e5+1;
const int inf=1e9;
int main(){
	int N;long K; cin>>N>>K;
	int A[N]; pair<int,int> g[N];
	rep(i,0,N) cin>>A[i];
	int id[size];
	rep(i,0,size) id[i] = -1;
	rep(i,0,2*N){
		int a = A[i % N];
		if(id[a] == -1) id[a] = i;
		else{ g[id[a] % N] = {i % N, (id[a] < N & N <= i)}; id[a] = i; }
	}
	int l = 0; int v = 0;
	while(true){
		l += g[v].second;
		v = g[v].first + 1;
		if(v == N) break;
	}
	K %= l + 1; l = 0; v = 0;
    if(K == 0) return 0;
	while(true){
        if(l == K - 1) break;
		l += g[v].second;
		v = g[v].first + 1;
	}
	deque<int> dq;
	while(v < N){
		if(v < g[v].first) v = g[v].first + 1;
		else{ dq.push_back(A[v]); v++; }
	}print(dq,,dq.size());
}