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;
#define re register
int a[2000100],b[2000100],c[2000100],b1[2000100],c1[2000100],q[2000100],ta;
bool bo[2000100];
int main()
{
	re int n,ans=1;re long long k;
	scanf("%d%lld",&n,&k);
	for(re int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		if(!b[a[i]])b[a[i]]=i;
	}
	c[n]=b[a[n]]+1;b1[a[n]]=n;c[n+1]=1;
	for(re int i=n-1;i;i--)
	{
		if(!b1[a[i]])
		{
			c[i]=b[a[i]]+1;
		}else
		{
			c[i]=c[b1[a[i]]+1];
		}b1[a[i]]=i;
	}k--;
	while(k)
	{
		if(k&1ll)ans=c[ans];
		for(re int i=1;i<=n+1;i++)c1[i]=c[c[i]];
		for(re int i=1;i<=n+1;i++)c[i]=c1[i];
		k>>=1;
	}
	for(re int i=ans;i<=n;i++)
	{
		if(!bo[a[i]])bo[a[i]]=1,q[++ta]=a[i];
		else
		{
			while(bo[a[i]])bo[q[ta]]=0,ta--;
		}
	}
	for(re int i=1;i<=ta;i++)printf("%d ",q[i]);
}