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 <cstdio>
#include <cstring>

int d[300000],g[300000],q[300000],r[300000];
int i,k,n,p;
long long m;

int main()
{
	scanf("%d%lld",&n,&m);
	for (i=1;i<=n;i++)
		scanf("%d",&g[i]);
	for (i=n;i>0;i--)
	{
		if (d[g[i]])
			r[i]=d[g[i]]+1;
		d[g[i]]=i;
	}
	for (i=n;i>0;i--)
		if (! r[i])
			r[i]=d[g[i]]+n+1;
	for (p=r[1];;p=r[p])
	{
		while (p>n)
			p=p-n,k++;
		if (p==1)
			break;
	}
	m=m%k;
	if (! m)
		return 0;
	for (p=1,k=1;;p=r[p])
	{
		while (p>n)
			p=p-n,k++;
		if (k==m)
			break;
	}
	memset(d,0,sizeof(d));
	for (k=0;p<=n;p++)
		if (d[g[p]])
			while (d[g[p]])
				d[q[k]]=0,k--;
		else
			k++,q[k]=g[p],d[g[p]]=1;
	for (i=1;i<=k;i++)
		printf("%d ",q[i]);
	return 0;
}