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;
typedef long long LL;
int n,a[200005],nt[200005],t[200005];
LL m;
#define INF 0x3f3f3f3f
vector<int>g[200005];
bool f[200005];
int main()
{
	scanf("%d%lld",&n,&m);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		g[a[i]].push_back(i);
	}
	for(int i=1;i<=n;i++)
		if(!f[a[i]])
		{
			f[a[i]]=1;
			int x=a[i];
			for(int j=1;j<g[x].size();j++)
				nt[g[x][j-1]]=g[x][j];
			nt[*(g[x].end()-1)]=g[x][0];
		}
	int x=1;
	LL k=0;
	while(1)
	{
		int x1=nt[x];
		if(x1<=x)
			k+=n-x+1+x1;
		else
			k+=x1-x+1;
		if(x1==n)
			break;
		x=x1+1;
	}
	m=m*n%k;
	x=1,k=0;
	while(m)
	{
		int x1=nt[x];
		if(x1<=x)
		{
			k+=n-x+1+x1;
			if(k>=m)
			{
				k-=n-x+1+x1;
				break;
			}
		}
		else
		{
			{
				k+=x1-x+1;
				if(k>=m)
				{
					k-=x1-x+1;
					break;
				}
			}
		}
		x=x1+1;
		if(x>n)
			x-=n;
	}
	m-=k;
	memset(f,0,sizeof(f));
	int sta=0;
	if(m==0)
		return 0;
	m--;
	t[++sta]=a[x];
	f[a[x]]=1;
	while(m)
	{
		m--,x++;
		if(x>n)
			x-=n;
		if(!f[a[x]])
			f[a[x]]=1,t[++sta]=a[x];
		else
		{
			while(t[sta]!=a[x])
				f[t[sta--]]=0;
			f[t[sta--]]=0;
		}
	}
	for(int i=1;i<=sta;i++)
		printf("%d ",t[i]);
}

