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>
typedef long long LL;

const int N=200005;

int n,a[N],b[N],pts[N],pre[N],nxt[N];
bool vis[N];
LL m;

int main()
{
	scanf("%d%lld",&n,&m);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	for (int i=n;i>=1;i--)
	{
		nxt[i]=pre[a[i]];pre[a[i]]=i;
		if (!nxt[i]) pts[i]=i;
		else pts[i]=pts[nxt[i]+1];
	}
	if (pts[1]==0) return 0;
	int x=1,tot=0;
	while (1)
	{
		if (vis[x]) break;
		b[++tot]=x;
		vis[x]=1;
		if (x) x=pre[a[pts[x]]]+1;
		else x=1;
		if (x>n) x=0;
	}
	if (m>tot)
	{
		int l=1;
		while (b[l]!=x) l++,m--;
		m=(m-1)%(tot-l+1)+1;
		m+=l-1;
	}
	for (int i=pts[b[m]];i;i=pts[i+1]) printf("%d ",a[i]);
	return 0;
}