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 sz(c)      int(c.size())
#define rep(i,a,b) for (int i=a; i<(b); ++i)
#define per(i,a,b) for (int i=(b)-1; i>=(a); --i)
using namespace std;
using ll = long long;

int const DSZ=6;
int const MAXN=220000;
int N;
ll K;
int pr[MAXN],nx[MAXN],len[MAXN];
ll last[MAXN];
int s[MAXN];
int ss;

int main() {
	cin.tie(0);
	ios_base::sync_with_stdio(0);
	cout<<fixed<<setprecision(10);

	cin>>N>>K;
	vector<int> a(N);
	rep(i,0,N) cin>>a[i];
	
	rep(i,0,N) pr[a[i]]=-1;
	rep(i,0,2*N) {
		int cur=a[i%N];
		if (pr[cur]!=-1 && pr[cur]<N) {
			nx[pr[cur]]=(i+1)%N;
			len[pr[cur]]=i+1-pr[cur];
		}
		pr[cur]=i;
	}
	
	K*=N;
	rep(i,0,N) last[i]=-1;
	int cur=0;
	while (K>len[cur]) {
		if (last[cur]!=-1) {
			K%=last[cur]-K;
			if (K<len[cur]) break;
		}
		
		last[cur]=K;
		K-=len[cur];
		cur=nx[cur];
	}
	
	map<int,int> pos;
	ss=0;
	while (K>0) {
		int p=pos[a[cur]];
		if (p<ss && s[p]==a[cur]) {
			ss=p;
		} else {
			s[ss++]=a[cur];
			pos[a[cur]]=ss-1;
		}
		cur=(cur+1)%N;
		K--;
	}
	
	rep(i,0,ss) cout<<s[i]<<" \n"[i+1==ss];
}
