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 ll long long
using namespace std;
const int N=2e5+10;
int n;
long long k;
int a[N],las[N],pos[N],b[N],len[N];
bool c[N];
int main() {
	scanf("%d%lld",&n,&k);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	for (int i=n;i>=1;i--) las[i]=pos[a[i]],pos[a[i]]=i;
	for (int i=1;i<=n;i++) if (!las[i]) las[i]=pos[a[i]],len[i]=1;
	for (int i=1;i<=n;i++) if (las[i]==n) len[i]++;
	for (int i=1;i<=n;i++) las[i]=las[i]%n+1;
	int now=1,l=0; k--;
	while (k>0) {
		k-=(ll)len[now]; now=las[now];
		if (c[now]) break;
		c[now]=1; b[++l]=now;
	}
	if (k<0) return 0;
	if (k>0){
		int s=0;
		for (int i=1;i<=l;i++) if (b[i]==now) {
			for (int j=i;j<=l;j++) s+=len[b[j]]; break;
		}
		k=k%(ll)s;
		while (k>0) {
			k-=(ll)len[now]; now=las[now];
		}
		if (k<0) return 0;
	}
	memset(pos,0,sizeof(pos)); l=0;
	for (int i=now;i<=n;i++) if (!pos[a[i]]) {
		pos[a[i]]=i; b[++l]=a[i];
	} else {
		while (b[l]!=a[i]) pos[b[l]]=0,l--;
		pos[a[i]]=0; l--;
	}
	for (int i=1;i<=l;i++) printf("%d ",b[i]);
} 