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<stdio.h>
#include<iostream>
#include<algorithm>
#include<queue>
#include<string.h>
using namespace std;
int n,a[200005],fa[46][200005],u,l[200005],p[200005],s[200005],ins[200005],top,i,j;
long long k,leng[46][200005];
int main()
{
	scanf("%d",&n);
	cin>>k;
	for(i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		if(l[a[i]]==0)
			l[a[i]]=i;
		if(i==n)
			leng[0][p[a[i]]]++;
		fa[0][p[a[i]]]=i%n+1;
		p[a[i]]=i;
	}
	for(i=1;i<=n;i++)
		if(fa[0][i]==0)
		{
			fa[0][i]=l[a[i]]%n+1;
			leng[0][i]=1;
			if(l[a[i]]==n)
				leng[0][i]++;
		}
	for(i=1;i<=45;i++)
		for(j=1;j<=n;j++)
		{
			fa[i][j]=fa[i-1][fa[i-1][j]];
			leng[i][j]=leng[i-1][j]+leng[i-1][fa[i-1][j]];
		}
	u=1;
	for(i=45;i>=0;i--)
		while(k>leng[i][u])
		{
			k-=leng[i][u];
			u=fa[i][u];
		}
	while(1)
	{
		if(u>n)
		{
			u=1;
			k--;
		}
		if(k==0)
			break;
		if(ins[a[u]])
			while(ins[a[u]])
			{
				ins[s[top]]=0;
				top--;
			}
		else
		{
			s[++top]=a[u];
			ins[a[u]]=1;
		}
		u++;
	}
	for(i=1;i<=top;i++)
		printf("%d ",s[i]);
}
